Apparatus for incoherent/coherent readout and display of information stored in double angularly multiplexed volume holographic optical elements

ABSTRACT

Apparatus is provided for the readout, and in certain applications the display, of information stored within incoherent/coherent double angularly multiplexed volume holographic optical elements. Such multiplexed volume holographic optical elements are based on parallel incoherent/coherent double angularly multiplexed volume holographic recording and readout principles, and are designed to exhibit maximum optical throughput efficiency and minimum crosstalk. Applications for this novel holographic readout apparatus, when used in conjunction with the aforementioned incoherent/coherent double angularly multiplexed volume holographic optical elements, include photonic interconnections for neural networks, telecommunications switching, and digital computing; optical information processors and optical memories; and optical display systems. The holographic readout apparatus is based primarily on the use of a spatially distributed source array, which contains a plurality of optical sources that are at once both individually coherent and mutually incoherent. The incorporation of the incoherent/coherent source array enables embodiments of the apparatus that in turn allow for incoherent superposition of reconstructed images and simplified parallel readout of the multiplexed volume holographic optical elements. The additional provision of spatial light modulation means allows for independent selection of the subset of stored holographically-encoded information patterns to be simultaneously read out or displayed. The holographic readout apparatus is capable of reading out and displaying information stored in several variants of incoherent/coherent double angularly multiplexed volume holographic optical elements, including those that are either optically recorded or computer generated, and that are based on either continuous-volume (bulk) or stratified-volume holographic media.

ORIGIN OF INVENTION

The U.S. Government has certain rights in this invention pursuant toContract No. F49620-87-C0007, awarded by the Department of the AirForce, and to Grant No. AFOSR-89-0466, awarded by the Defense AdvancedResearch Projects Agency through the Department of the Air Force.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a divisional application of Ser. No.08/441,333, filed May 15, 1995, now U.S. Pat. No. 5,661,577, which inturn a divisional application of Ser. No. 07/894,825, filed Jun. 8,1992, now U.S. Pat. No. 5,416,616, issued May 16, 1995, which in turn isa continuation-in-part application of Ser. No. 07/505,790, filed Apr. 6,1990 now U.S. Pat. No. 5,121,231, issued Jun. 9, 1992.

TECHNICAL FIELD

The present invention relates to multiplexed volume holographicrecording, readout, and interconnections, and, more particularly, tophotonic interconnections, photonic implementations of neural networks,optical signal processing, optical information processing and computing,optical memory, optical displays, copying of multiplexed volumeholograms, and multiplexed volume holographic optical elements.

BACKGROUND ART

A wide variety of information systems applications exist that require ahigh density of interconnections among device or system nodes, or a highdensity of rapidly accessible memory, or both. These applicationsinclude, for example, neural networks, telecommunications switchingsystems, digital computing, and information (including signal)processing. In many such applications, key requirements on the choseninterconnection technology include low insertion losses, highinterchannel isolation (freedom from inter-channel crosstalk), a highdegree of potential fan-in and fan-out at each node, weightedinterconnection channels, and high capacity. Comparable requirementsexist for the chosen memory technology, including low latency (rapidinformation access), parallel information retrieval, low effective biterror rates (high signal-to-noise ratio), high density informationstorage, and input/output compatibility with the remainder of thesystem.

In order to satisfy these many and varied requirements, multiplexedvolume holographic optical elements provide an attractive alternative toelectronic implementations of high capacity interconnection and memoryelements. In fact, the very nature of a volume holographic opticalelement tends to blur the distinction between a pure interconnectionnetwork on the one hand, and a pure memory sub-system on the other, asit is in many ways simultaneously well-suited to both roles. Even so,previous methods for recording information or interconnection patternsin highly multiplexed volume holographic optical elements, and forreading them out, have not proven satisfactory in terms of throughput,crosstalk, and capacity. Furthermore, they have not proven to bemanufacturable, due to the fact that information from a master volumeholographic optical element could not previously be efficientlytransferred to or duplicated in another such element.

In forming multiplexed volume holograms, one of three approaches istypically taken: (1) sequential, which involves severaltemporally-sequenced (and hence incoherent) exposures of the individualcomponents of the hologram, done by rotating or translating the hologram(or the source beam, reference beam, or object beam); (2) simultaneousand fully coherent, which involves the use of two or more mutuallycoherent beams, each encoded with information and serving as a referencebeam for the other(s); and (3) some combination of sequential andsimultaneous fully coherent.

The first approach has the major disadvantage that temporal sequencingis time-consumptive, which can be of considerable importance inapplications envisioned herein, for which the number of independentinterconnections that must be recorded is extremely large. Also, in manyholographic recording materials, sequential exposures tend to erasepreviously recorded information, leading to the necessity ofincorporating unwieldy programmed recording sequences in order to resultin the storage of a predetermined set of interconnections.

The second approach is designed to circumvent the above sequencingdifficulties, but suffers instead from the coherent recording ofunwanted interference patterns (holograms) that give rise to deleteriouscrosstalk among the various (supposedly independent) reconstructions, asdescribed in more detail below.

The third approach is subject both to sequential recording time delaysand the necessity for programmed recording schedules, as well as to thegeneration of undesirable crosstalk. As such, none of the previouslyemployed multiplexed recording techniques allows for the generation ofthree-dimensional, truly independent interconnections between two ormore two-dimensional planar arrays within the context of a temporallyefficient recording scheme.

In all of the prior art approaches to the holographic recording of amultiplexed interconnection, two primary forms of interchannel crosstalkare encountered to a greater or lesser extent. Coherent recordingcrosstalk arises from the simultaneous use of multiple object andreference beams, all mutually coherent with each other. The mutualcoherence causes additional interconnections to be formed other thanthose desired. Reconstruction with independently valued inputs resultsin the generation of output beams that cross-couple through theundesired interconnection pathways, which compromises the independenceof the desired interconnection channels.

A second, unrelated form of crosstalk arises due to beam degeneracy,which occurs whenever a single object beam is used with a set ofreference beams to record a fan-in interconnection to a single outputnode (e.g., neuron unit in the case of the photonic implementation ofneural networks). (Fan-in is the connection of multiple interconnectionlines to a common output node.) This latter form of crosstalk is presenteven when the set of object beams is recorded sequentially.

Of at least equally serious consequence is the optical throughput lossthat results from interconnection fan-in so constructed as to exhibitbeam degeneracy. In many well-documented cases, this loss is severe,resulting in at least an (N-1)/N loss (or, equivalently, a 1/Nthroughput efficiency) for the case of an N-input, N-outputinterconnection system, as reported by J. W. Goodman, Optica Acta, Vol.32, pages 1489-1496 (1985). This is a truly daunting loss factor forinterconnection systems such as those envisioned for neural networks,which may both require and be capable of 10⁵ to 10⁶ inputs and outputs.

In certain types of photorefractive materials, an additional throughputloss can arise from the incoherent superposition of several gratingswithin the same volume of the holographic optical element, due to thereduction in the effective modulation depth of the recorded holographicfringes. This effect occurs primarily in photorefractive crystals thatgenerate an index of refraction or absorption change in response tolocal gradients in the intensity distribution, but would not be expectedto occur in linear photorefractive materials that generate an index ofrefraction or absorption change in direct proportion to the magnitude ofthe local intensity distribution. In a number of cases, this effect canalso result in at least an (N-1)/N loss for the case of an N-input,N-output interconnection system, as reported by P. Asthana, "VolumeHolographic Techniques for Highly Multiplexed InterconnectionApplications", Ph.D. Dissertation, University of Southern California(1991), available from University Microfilms, Ann Arbor, Mich.

In the prior art, few attempts have been made to address the extremelyimportant technological problem of duplicating the contents of a fullyrecorded, heavily multiplexed volume holographic optical element orinterconnection device, particularly in the case of neural networkinterconnections. For example, to the inventors' knowledge, there is noknown prior technique for rapid copying of a volume hologram that isangularly multiplexed in two dimensions, other than that described inthe parent application of the present application.

In the case of neural network interconnections, the training and/orlearning sequences may be quite involved; in some cases, the trainingand/or learning sequences may result in a unique interconnection, andthe exact learning sequence may not be reproducible in and of itself atall. In such cases, it is desirable to replicate the contents of theinterconnection medium in such a manner that a fully functional copy isproduced, as characterized by a complete operational set ofinterconnections indistinguishable from those implemented by the master.The method of replication must not demand an extremely lengthy recordingsequence, must not be inefficient in its utilization of the programmedrecording schedule and/or the total optical energy available forreproduction purposes, and must not induce additional optical throughputloss or interchannel crosstalk beyond that already incorporated in themaster.

In the grandparent application of the present application,"Incoherent/Coherent Multiplexed Holographic Recording for PhotonicInterconnections and Holographic Optical Elements", now issued as U.S.Pat. No. 5,121,231, (Jun. 9, 1992), apparatus for theincoherent/coherent multiplexed holographic recording of photonicinterconnections and holographic optical elements is described.Specifically, apparatus for providing multiplexed volume holographicrecording and readout comprises:

(a) means for providing an array of coherent light sources that aremutually incoherent;

(b) means for simultaneously forming an object beam and a reference beamfrom each coherent light source, thereby forming a set of multiplexedobject beams and a separate set of multiplexed reference beams;

(c) means for either independently modulating each object beam, orspatially modulating a set of object beams so that all object beams areidentically modulated;

(d) means for either independently modulating each reference beam, orspatially modulating a set of reference beams so that all referencebeams are identically modulated;

(e) a holographic medium capable of simultaneously recording therein aholographic interference pattern produced by at least a portion of theset of all modulated multiplexed object beams and of the set of allmodulated multiplexed reference beams pairwise, with all such pairsbeing mutually incoherent with respect to one another; and

(f) means for directing at least a portion of the set of modulatedobject beams and of the set of modulated reference beams onto theholographic medium and for interfering the portion of the modulatedobject beams and of the set of modulated reference beams, pairwise,inside the holographic medium.

Although the primary mode of multiplexing is angular, spatial and/orwavelength multiplexing may also be incorporated.

The architecture and apparatus described in the grandparent applicationsignificantly reduce coherent recording crosstalk and beam degeneracycrosstalk, and permit simultaneous network initiation, simultaneousweight updates, and incoherent summing at each output node withoutsignificant fan-in loss.

Further in accordance with the grandparent application of the presentapplication, the above apparatus is provided with means for controllablyblocking the set of object beams such that at least a portion of the setof reference beams (either modulated or unmodulated) reconstruct astored holographic interference pattern. In one embodiment, thereconstructed pattern is angularly multiplexed and detected in such amanner as to produce an incoherent summation on a pixel-by-pixel basisof the reconstructed set of object beams. In this manner, multiplexedvolume holographic recording and readout are provided.

Specific implementations to neural networks, telecommunicationinterconnections (e.g., local area networks and long distanceswitching), interconnections for digital computing, and multiplexedholographic optical elements are provided in both the grandparent andthe parent applications.

In addition, apparatus for copying a multiplexed volume hologram isprovided in the grandparent application. The apparatus comprises:

(a) means for providing an array of coherent light sources that aremutually incoherent;

(b) means for forming two reference beams from each coherent lightsource, thereby forming two sets of multiplexed reference beams, eachset at a different location;

(c) means for directing the first set of reference beams onto theoriginal multiplexed volume hologram to thereby form a set of outputbeams;

(d) means for directing the second set of reference beams onto asecondary holographic recording medium;

(e) means for directing the set of output beams from the originalmultiplexed volume hologram onto the secondary holographic recordingmedium, with path lengths sufficiently identical to the reference beampath lengths to permit coherent interference, pairwise, between theoutput beams and the second set of reference beams, inside the secondaryholographic recording medium; and

(f) means for simultaneously recording in the secondary holographicmedium a holographic interference pattern produced by the set of outputbeams and the second set of reference beams, thereby forming thesubstantially identical multiplexed volume hologram.

Portions of the above-described apparatus also possess unique propertiesand give rise to useful functions. It is to these unique portions, orelements, that the present application is directed.

In addition, specific implementations are given that utilize subhologramformation to avoid throughput losses due to incoherent superpositioneffects, that provide for various modes of information transfer from amaster hologram to a copy, that address application areas in opticalmemory and optical signal processing, and that exploit the doubleangular multiplexing features of the apparatus described in thegrandparent and parent applications.

DISCLOSURE OF INVENTION

In accordance with the invention, a multiplexed volume holographicelement comprises a volume holographic medium capable of storing aholographic modulation pattern, the holographic modulation patterncomprising a multiplexed set of modulation pattern components, each ofwhich, when illuminated by an associated reference beam, leads to areconstructed beam such that:

(a) the reconstructed beams that emanate from the holographic medium areat least partially angularly multiplexed;

(b) a spatial array of pixels is encoded onto each reconstructed beam,as an image at some plane in space; and

(c) the images of said spatial arrays of pixels from the reconstructedbeams can be made to be substantially coincident in space.

Such multiplexed holographic elements in accordance with the teachingsof the invention can be generated by optically recording a holographicinterference pattern in output beam and each corresponding referencebeam, inside the secondary holographic medium; and

(d) means f or recording in the secondary holographic medium aholographic interference pattern produced by the set of output beams andthe portion of each beam of the set of mutually incoherent referencebeams.

Also provided are means for transferring information from the secondaryholographic medium to the primary holographic medium, thereby enablingiterative feedback between the two holographic media.

Further in accordance with the invention, apparatus for double angularmultiplexing is provided, comprising means for directing a set ofself-coherent but mutually incoherent beams to a spatial modulationmeans for spatially modulating the set of beams, the spatial modulationmeans comprising a plurality of pixels, at least one of which pixels iscommon to more than one beam, with each beam that shares the commonpixel being angularly multiplexed at the common pixel.

Provision is further given for the spatial modulation means to compriseat least one of a spatial light modulator, a planar hologram, and avolume hologram.

Specific implementations are provided to: optical interconnections inneural networks, digital computing, and telecommunications; holographicoptical elements; optical information processing; and optical memory.

In accordance with the invention, a multiplexed volume holographicoptical element readout apparatus is provided, comprising:

(a) means for providing a two-dimensional array of individually coherentlight sources that are mutually incoherent;

(b) means for forming a reference beam from each individually coherentlight source within the source array, thereby forming a multiplexed setof reference beams;

(c) means for modulating each reference beam, thereby forming amultiplexed set of modulated reference beams;

(d) means for securing and orienting a volume holographic opticalelement in a predetermined location; and

(e) means for directing at least a portion of the multiplexed set ofmodulated reference beams to the predetermined location.

As such, the apparatus of the invention provides for the readout anddisplay of information stored in incoherent/coherent double angularlymultiplexed volume holographic optical elements by utilizing an array ofindividually coherent light sources that are mutually incoherent, meansfor selectively modulating the reference beam generated by each suchsource, and means for directing at least some of these reference beamsto a predetermined location where further means are disposed forsecuring and orienting any of a number of incoherent/coherent doubleangularly multiplexed volume holographic optical elements. Specificmeans for providing the requisite 2-D source array are described,including a 2-D array of semiconductor laser diodes (for example, anarray of vertical cavity surface emitting lasers (VCSELs); and a set ofdiffraction gratings, each of a different frequency, propagating in anacousto-optic cell.

Further in accordance with the invention, a multiplexed volumeholographic optical element readout apparatus is provided, comprising:

(a) means for providing an array of coherent light sources that aremutually incoherent, which means further comprise:

(i) provision for inputting at least one coherent beam,

(ii) a first acousto-optic deflector, storing a set of moving gratings,each grating having a different spatial frequency, and

(iii) means for directing at least one coherent beam onto the firstacousto-optic deflector, thereby generating a set of output beams;

(b) means for forming a reference beam from each coherent light sourcewithin the source array, thereby forming a multiplexed set of referencebeams;

(c) means for modulating each reference beam, thereby forming amultiplexed set of modulated reference beams;

(d) means for securing and orienting a volume holographic opticalelement in a predetermined location; and

(e) means for directing at least a portion of the multiplexed set ofmodulated reference beams to the predetermined location.

Provision is further given for the spatial modulation means to compriseat least one of a spatial light modulator, a planar hologram, and avolume hologram. Provision is also given for the addition of a secondacousto-optic deflector, oriented orthogonally to the first, to generateoutput beams that are angularly multiplexed in two dimensions.

Specific implementations are provided to: optical interconnections inneural networks, digital computing, and telecommunications; holographicoptical elements; optical information processing; and optical memory.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a generalized interconnection, with both fan-out and fan-in;

FIG. 2 is a schematic diagram of fan-out, showing interconnectionpathways and the implementation of analog weights;

FIG. 3 is a schematic diagram of fan-in, showing interconnectionpathways and the implementation of analog weights;

FIG. 4 is a schematic diagram of optical apparatus for simultaneousincoherent/coherent recording of multiplexed holograms, showing angularmultiplexing of the reference beam set;

FIG. 5 is a schematic diagram of optical apparatus for eithersimultaneous or independent readout of multiplexed holograms showingmutual incoherence of readout (reconstructed) beams;

FIG. 6A is a schematic diagram of optical apparatus for recording ofdouble angularly multiplexed holograms, each a hologram of a 2-D arrayof pixel values, while FIG. 6B is a schematic diagram of that portion ofthe apparatus of FIG. 6A used in the reconstruction of the recordedimages, showing the incoherent summation on the output plane of the setof reconstructed images in pixel-by-pixel registry, FIG. 6C is aschematic diagram of an acousto-optic deflector based system thatgenerates an array of coherent but mutually incoherent source beams, asneeded in the apparatus of FIGS. 6A and 6B;, and FIG. 6D is a schematicdiagram of a simplified optical apparatus for incoherent/coherentreadout and display of double angularly multiplexed holograms, utilizingthe basic principles for reconstruction of the recorded images depictedin FIG. 6B.

FIGS. 7A-F show schematic diagrams of optical apparatus for one-stepcopying or information transfer from a primary multiplexed volumeholographic optical element to a volume holographic medium to yield asecondary multiplexed volume holographic optical element, with FIG. 7Adepicting apparatus for the case of two transmission holographicelements, FIG. 7B depicting apparatus for the case of two reflectionholographic elements, FIG. 7C depicting apparatus for the case of areflection primary holographic element and a transmission secondaryholographic element, FIG. 7D depicting apparatus for the case of atransmission primary hologram and a reflection secondary hologram, FIG.7E depicting apparatus for the case in which both holographic elementscomprise hybrids of transmission and reflection holograms, and FIG. 7Fdepicting apparatus for two-way information transfer between the twovolume holographic media, yielding a resonator arrangement;

FIG. 8 is a schematic diagram of the optical interconnection paths dueto a holographic interconnection architecture for the 3:3 fan-out/fan-incase, constructed such that each input and output node is only singlyangularly encoded, showing the origin of crosstalk and throughput lossdue to beam degeneracy;

FIG. 9, on coordinates of diffraction efficiency and normalized gratingstrength (v/π), is a simulation result for the holographicinterconnection architecture of FIG. 8 utilizing the optical beampropagation method, for the case of sequential recording of theinterconnection gratings, showing the fan-out loss;

FIG. 10, on coordinates of diffraction efficiency and normalized gratingstrength (v/π), is a simulation result for the holographicinterconnection architecture of FIG. 8 utilizing the optical beampropagation method, for the case of simultaneous fully coherentrecording of the interconnection gratings, showing the fan-outthroughput loss and the occurrence of recording-induced crosstalk;

FIG. 11 is a schematic diagram of optical interconnection paths of theapparatus described in FIG. 6 for the 3:3 fan-out/fan-in case, showingthe angular multiplexing of both object (source) and reference beamsets, configured to produce angular multiplexing of the reconstructionbeam fan-in to a given output node;

FIG. 12 is a schematic diagram of a multi-function spatial lightmodulator, as utilized in the interconnection architecture shown in FIG.14, showing the incorporation of multiple photosensitive elements,control electronics, and multiple modulation elements within each pixel;

FIG. 13, on coordinates of voltage (ordinate) and voltage (abscissa), isa plot of the output transfer characteristic curves for both outputs ofa dual rail CMOS differential amplifier, with 15 transistors in an areaof 2500 μm² ;

FIG. 14 is a schematic diagram of a preferred embodiment of apparatusfor the implementation of neural network modules, for the case ofHebbian learning;

FIG. 15 is a schematic diagram of a preferred embodiment of apparatusfor the implementation of neural network modules, for learningalgorithms of the form Δw_(ij) =αx_(i) δ_(j) ;

FIGS. 16A-C are schematic diagrams of preferred embodiments of means forgenerating learning terms δ_(i), for the cases of (A) Widrow-Hoff, (B)Perceptron, and (C) back propagation learning;

FIG. 17 is a schematic diagram of an alternative embodiment of apparatusfor the implementation of neural network modules;

FIG. 18 is a schematic diagram of apparatus for switching from a set ofwavelength division multiplexed optical input lines to a set ofwavelength division multiplexed optical output lines, wherein the sourcearray and two spatial light modulators are used to control the routingof the switch;

FIG. 19A is a schematic diagram of means for providing the source arrayof FIG. 18 in the case of a 1-D wavelength division multiplexed (WDM)input line array and a 1-D wavelength division multiplexed output linearray, showing the center optical frequency ν increasing along onedirection and the incorporation of mutual incoherence within a frequencyband Δν about each central optical frequency ν along a different,substantially orthogonal direction, while FIG. 19B is a schematicdiagram of an alternative embodiment utilizing a one-dimensional sourcearray, with center frequency of each element being different, and aone-dimensional phase modulator array providing mutual incoherence;

FIG. 20 is a schematic diagram of means for providing the source arrayof FIG. 18 in the case of a 2-D WDM input line array and a 2-D WDMoutput line array, showing a 2-D laser diode array each element of whichhas a different center frequency, and a modulator array;

FIG. 21 is a schematic diagram of method and apparatus for recording ofmultiplexed volume holographic optical elements, with one set of beamsmodulated independently and the other set of beams modulated spatiallybut identically; and

FIG. 22 is a schematic diagram of method and apparatus for recording ofmultiplexed volume holographic optical elements, with both sets of beams(reference and object) modulated independently.

BEST MODES FOR CARRYING OUT THE INVENTION A. GENERAL

1. Introduction.

The description that follows is primarily directed to neural networks.However, it will be appreciated by those skilled in the art that a majorcomponent of the architecture and apparatus is generic to a number oftechnologies, including telecommunications, digital computing, opticalinformation processing and computing, optical memory, copying ofmultiplexed volume holograms, and holographic optical elements. Specificapplications to these technologies are discussed below.

In considering the teachings of the invention, it is essential todifferentiate between two basic types of optical interactions (asdetermined by the nature of the optical signals involved): incoherentand coherent. Incoherent interactions occur whenever the input signalstemporally dephase over the relevant time of observation (detectortemporal integration window), in that they are either broadband (notmonochromatic) or are narrow band (nearly monochromatic) but separatedin optical frequency by more than the inverse of the observation time.

Interactions in which the input optical signals spatially dephase overthe spatial aperture of the relevant detector wherever the output isutilized (detector spatial integration window) are also incoherent forall practical purposes, and will obey certain summation rules. Coherentinteractions occur, on the other hand, whenever the input signalssimultaneously maintain a constant phase relationship over the detectorspatial and temporal integration windows.

From these remarks, it can be seen that it is quite important tounderstand the distinction between coherent (or incoherent) light andcoherent (or incoherent) interactions as defined by the eventualdetector configuration and operational parameters. For example, it isperfectly acceptable to consider a situation in which two mutuallycoherent (temporally) optical beams interact to produce an interferencepattern with a spatial scale small compared with the relevant detectoraperture. For two such mutually coherent optical beams propagating at anangle with respect to each other, the spatial scale of the resultantinterference pattern decreases as the angle between the two beamsincreases. In such cases, the interaction will in fact follow incoherentsummation rules, as the detector effectively integrates the spatiallyvarying interference pattern to produce exactly the same result as theinteraction of two mutually incoherent (temporally) optical beams.

Referring now to the drawings, wherein like numerals of referencedesignate like elements throughout, FIG. 1 depicts a generalizedinterconnection scheme, showing both fan-in of input beams 10, 10' tonodes 12, 12', respectively, and fan-out of output beams 10', 10" fromthe nodes.

The section of the interconnection shown depicts the fan-in to them^(th) node from the (m-1)^(th) node plane (not shown), a fullyconnected layer in which the interconnections fan out from each node 12labeled 1 through N to the nodes labeled correspondingly 1 through N inthe (m+1)^(th) node plane wherein full fan-in is effected, and fan-outfrom the (m+1)^(th) node plane to the (m+2)^(th) node plane (not shown).In some interconnection schemes, the m^(th) node plane and the(m+1)^(th) node plane are one and the same, consisting therefore of aset of nodal outputs fully interconnected to the corresponding set ofnodal inputs in a feedback arrangement.

The weights w_(ij) are shown to indicate that each (analog)interconnection path modifies the output from a given node by means ofthe multiplication weight w_(ij) before fan-in is performed with anappropriate summing operation at each node input. The weight labelingscheme employed is as shown, such that the weight w_(ij) interconnectsthe j^(th) nodal output in a given plane to the ith nodal input in thesucceeding plane.

FIG. 2 depicts fan-out of a plurality of output beams 10' from a node 12(i.e., the i^(th) node) on which at least one input beam 10 is incident.Each beam 10' is propagated to the next node with a separate andindependent analog weight w_(ij) as noted above, which is assigned toeach interconnection path.

As depicted in FIG. 2, for the purposes of this invention, the outputvalue from each given node is common, such that the interconnectionsrepresent true fan-out rather than the individual interconnection ofmultiple output ports from a single node.

FIG. 3 depicts fan-in of a plurality of input beams 10 to node 12,generating at least one output beam 10'. Each beam 10 is modified by aseparate and independent analog weight w_(ij), assigned to eachindependent interconnection path. True fan-in is achieved by means of anappropriate summation rule at a single node input, as shown in theFigure. Pertinent to the invention described in this application, suchfan-in can be provided by a set of optical beams that are incident on acommon detector plane, each incident at a separate angle.

In FIGS. 1, 2, and 3, the triangular symbol utilized to depict eachinterconnection node represents not only the indicated direction of dataflow through the node, but also the potential for incorporation of aninput-to-output control transfer function (e.g., a hard or softthreshold in the case of a neural network) that operates on thefanned-in, summed inputs to produce a single (usually analog) outputvalue that is fanned out in turn to the succeeding network stage.

FIGS. 4 and 5 depict schematically how recording (FIG. 4) andreconstruction (FIG. 5) of a set of holograms is accomplished inaccordance with the invention described in the grandparent application.In FIG. 4, an array of coherent but mutually incoherent sources 14generates a set of beams 10 (two such beams 10a, 10b are shown). Abeamsplitter 16 forms a set of object beams 11 and a set of referencebeams 13. The object beams 11 pass through a set of objects (A₁, A₂) 18to form a set of object-encoded beams 15, which impinge on element 20incorporating a holographic recording medium. As used herein, "20"represents a volume holographic optical element, comprising a volumeholographic medium and one or more holograms each consisting of amodulation pattern. It will be appreciated that in some cases, theelement 20 will not yet have recorded therein the holographic modulationpattern and thus will consist only of the holographic medium. Since theintent is to record such patterns into the medium, the element 20 ishereinafter referred to as a holographic element, even though it may nothave the holographic patterns recorded therein.

The reference beams 13 are reflected from a set of mirrors 22 and alsoimpinge on the holographic element 20, where they interfere with theobject-encoded beams 15 pairwise to form holographic interferencepatterns in the recording medium, as is well-known.

It will be noted that the foregoing apparatus permits simultaneousrecording of the objects. Further, a first light source 14a in thesource array 14 is used to generate a first set of two beams 11a and 13awhich are mutually coherent; these beams derive from beam 10a. A secondlight source 14b in the source array is used to generate a second set oftwo beams 11b and 13b, which are also mutually coherent; these beamsderive from beam 10b. However, since the two light sources 14a and 14bare mutually incoherent, then beams 10a and 10b are mutually incoherent,and the two sets of beams derived therefrom are also mutually incoherentand hence do not mutually interfere to form an interference pattern inthe medium of holographic element 20. While only two light sources 14a,14b are described, there is, of course, a plurality of such lightsources in the source array 14, each generating a coherent pair ofobject and reference beams, each pair incoherent with all other pairs.

It will be noted that the superposition of a set of optical interferencepatterns can be referred to as a set of mutually incoherent opticalinterference patterns if all of the pairs of beams that generate eachindividual optical interference pattern within the set are individuallycoherent but mutually incoherent. Likewise, the set of holographicrecords of a set of optical interference patterns can be referred to asa set of mutually incoherent holographic records if all of thecorresponding optical interference patterns within the set are mutuallyincoherent.

Finally, each of the set of object beams and each of the set ofreference beams is independently multiplexed in at least one of angle,space, and wavelength.

In FIG. 5, readout, or reconstruction, is achieved by blocking theobject beams 11. In the case of a holographic optical element, theholographic element 20 may be read out in a physically distinct opticalsystem, in which the reference beam phase fronts illuminating theholographic medium approximate those of the recording system. Readoutmay be simultaneous and independent, or individual.

Simultaneous and independent readout is characteristic, for example, ofneural networks, associative memories, and shared memories. Individualreadout, by contrast, is characteristic of conventional optical memorysystems.

In simultaneous and independent readout, output (reconstructed) beams10a' and 10b' are mutually incoherent, and complete control of what isread out is provided; that is, one-half of beam 13a and all of beam 13b,or all of beams 13a, 13b, and 13c (not shown), or other combinations maybe controllably used as readout beams, with the modified set ofreconstructed output beams incoherently superimposed in space. Forclarity, beam 13c is omitted from the drawing. If shown, it would be atyet a different angle from beams 13a and 13b.

In individual readout, any individual readout beam 13j can be modulatedand utilized to reconstruct an individual output beam 10a' or 10b' (or10c', etc.) without significant crosstalk.

Virtual images A₁ ' and A₂ ' are generated from the reconstructionprocess in the position designated 18' where the objects 18 were locatedduring the recording process, in such a manner that the reconstructions10' appear to emanate from the virtual images. As shown in FIGS. 4 and5, if the original objects 18 are located at separate positions inspace, then the virtual images 18' are also located at distinctpositions. It will thus be appreciated by one skilled in the art that inany subsequent image plane of virtual images 18', images of the objectsA₁, A₂, and the like will again be located at separate positions.Another key point is that the set of reconstructed beams 10' are allmutually incoherent, and hence obey incoherent summation rules in anychosen output plane.

FIG. 6A depicts apparatus suitable for the simultaneous recording ofdouble angularly multiplexed holograms, with each hologram representinga spatial comprising array of pixels. A shutter 24 in the path of theset of object beams 11 is used to control passage of the set of objectbeams to the holographic element 20. During recording, the shutter 24 isopen. The set of object beams 11 passes through a lens 26, whichapproximately collimates the set of beams and directs them toward afirst spatial light modulator (SLM) 28. Thus, each pixel of modulator 28has many mutually incoherent optical beams (angularly multiplexed)passing through it. (This feature is called simultaneous spatialmodulation of angularly multiplexed incoherent beams.) The resulting setof modulated beams {A_(j) } is incident on the holographic element 20.

The set of reference beams 13 passes through lens 30 and lens 34,reflecting from mirror 22 in the process; their function, together, isto focus each beam onto the corresponding pixel of modulator 32. Fromspatial light modulator 32, the set of reference beams 13 is directedinto the holographic element 20 by lens 36, where the reference beamsinterfere with the object beams pairwise to produce a multiplexedhologram with a set of stored interconnection weights. Theinterconnection weights can be dependent on corresponding products ofthe form A_(j) X_(j), as described in more detail below. The resultingmultiplexed hologram thus further comprises a set of subholograms, witheach subhologram formed by an individual pair of mutually coherentobject and reference beams.

Finally, it will be noted that the object beams 11 are all at differentangles with respect to each other and that the reference beams 13 arealso all at different angles with respect to each other. As aconsequence of this angular difference, it will be appreciated thatthese beams are double (meaning both object and reference beams)angularly multiplexed in the volume holographic element 20.

It will be further appreciated by those skilled in the art that theplacement of lens 36 determines whether the beams transmitted throughthe spatial light modulator 32 are collimated at the entrance plane ofthe hologram, focused at the entrance plane of the hologram to form animage of the spatial light modulator, or formed instead into expandingor contracting wavefronts at the entrance plane of the hologram. Asecond lens (not shown) placed following spatial light modulator 28 canbe adjusted to focus the two-dimensional Fourier transform of each ofthe beams transmitted through spatial light modulator 28 onto spatiallyseparated regions at the-entrance plane of the hologram. This samefunction can also be accomplished by appropriate choice and positioningof lens 26 without the need for a second lens.

Although many combinations of such configurations can be easily seen toexist, we define herein three preferred embodiments. In the "fullaperture" version of the architecture, both such lenses are adjusted tocollimate the beams transmitted by the spatial light modulatorssubstantially, filling the entire aperture of the holographic opticalelement. In the "non-overlapping subhologram" version of thearchitecture, the lens (not shown) following spatial light modulator 28is adjusted to focus the two-dimensional Fourier transform of each ofthe beams transmitted through spatial light modulator 28 onto spatiallyseparated regions at the entrance plane of the holographic opticalelement. In addition, lens 36 following spatial light modulator 32 isadjusted to image the output side of the spatial light modulator 32 ontothe entrance plane of the holographic optical element in such a manneras to assure registry of the image so generated with the array ofFourier transforms just described. In this manner, each individual pixelx_(j) is interconnected to the full set of pixels comprising spatiallight modulator 28. A third version of the architecture (the"overlapping subhologram" version) represents a compromise between thefull aperture and subhologram versions, and is obtained by placing thelenses in intermediate positions that result in overlapping subhologramswithin the holographic optical element. This version permitsoptimization of competing factors, including optical throughputefficiency, space-bandwidth product utilization, and numerical aperturerequirements on the optical components. It will be easily appreciated bythose skilled in the art that the use of lens location is but one ofmany means for implementing these various versions of the architecture.

FIG. 6B depicts the apparatus of FIG. 6A, but with the shutter 24closed, to permit reconstruction of the recorded holograms to generate aset of output beams 10', representing a set of virtual images 18', whichis passed through a lens 38 and imaged onto an output plane 40. Eachpixel of the superposition image in output plane 40 receives anintensity given by the incoherent summation of a number of terms, thenumber given by the fan-in to that pixel, which is equal to the numberof elements in the source array for the case of fully connectednetworks. Each individual term in the incoherent summation is in turnthe product of a stored interconnection weight w_(ij) multiplied by theintensity of the corresponding reference beam x_(j) during readout.Hence, the superimposed reconstructions of the separate stored holograms(generating the set of virtual images 18', which are substantiallycoincident in a region of pace as shown schematically in FIG. 6B) areincoherently summed pointwise (on a pixel-by-pixel basis in registry).

It should also be noted that lens 38 can be relocated to an appropriateposition between modulator 28 and holographic element 20. The apparatuswill then record holograms that reconstruct real (instead of virtual)images. As a result, no lenses are needed in the paths of the outputbeams 10' and the reconstructed arrays (which now represent real images)are still in registry in the output (real image reconstruction) plane.

It will be appreciated by those skilled in the art that variants of thisapparatus can be easily provided that are optimized for readout of thevolume holographic element only. As such, the source array 14 may beplaced at or near the indicated position of mirror 22, and beamsplitter16, shutter 24, lens 30, and mirror 22 can be eliminated. It will beobvious to those skilled in the art that this readout system includesmeans for securing and orienting the volume holographic element 20 atthe position and orientation shown. It will be further appreciated thatthe architecture as shown provides that the virtual images A_(j) aresuperimposed in space, so that they can in fact be imaged in registryonto a single output plane 40 as shown.

FIG. 6C depicts one embodiment of apparatus that generates an array ofself-coherent but mutually incoherent source beams, as provided bysource array means 14 of FIGS. 6A and 6B. A coherent laser source 240provides a single coherent beam 29 that is expanded via beam expander 31and lens 33, before being incident on acousto-optic deflector 35.Electronic circuitry 39 generates an electronic signal consisting of aset of N superimposed frequencies, each being an integral multiple of afundamental frequency. This signal can be generated by, for example, afrequency generator circuit that generates M frequencies, a series ofanalog multipliers, and one or more amplifiers. The multiplicationprocess results in a set of N=2^(M-1) superimposed frequencies, asdesired. This signal is sent into acousto-optic deflector 35 to generatea set of Mf superimposed diffraction gratings of different spatialfrequencies. Lens 37 then provides an optical spatial Fourier transformof the set of gratings, yielding an array of source beams 229. Becauseof the different frequencies of the gratings, the source beams 229comprise a spatial array of source beams that are individually coherentbut mutually incoherent. This source array generator can be used withcommon single laser sources, and provides flexibility in source spacingand in optical wavelength for laboratory use.

The incoherent/coherent recording technique described above and enabledby the source array reduces the number of spurious gratings written,thereby reducing crosstalk compared with fully coherent simultaneousrecording techniques. FIG. 6D depicts one embodiment of apparatus thatis optimized for incoherent/coherent readout and display of doubleangularly multiplexed volume holographic optical elements (withoutprovision for recording), as described above in reference to FIG. 6B,showing explicitly the simplification that results from removal of thecomponents used only for the recording function. As such, the sourcearray 14 has been placed at or near the indicated position of mirror 22,and beamsplitter 16, shutter 24, lens 30, and mirror 22 in FIG. 6B havebeen eliminated. Means 27 for securing and orienting a double angularlymultiplexed volume holographic optical element 20 are also shown. In thecase of FIG. 6D, the readout-only apparatus shown does not include thedouble angularly multiplexed volume holographic optical element 20 as anexplicit part of the apparatus, but instead allows for the insertion andremoval of any of a number of such incoherent/coherent double angularlymultiplexed volume holographic optical elements. Further, as in the caseof the recording and readout apparatus, it will be appreciated by thoseskilled in the art that alternative placements of lenses 34 and 36 canbe employed to provide different beam phase fronts at the aperture ofthe holographic optical element, thereby achieving readout based on thefull aperture, nonoverlapping subhologram, or overlapping subhologramversions of the architecture described above.

2. Source Array.

As discussed above, a critical and novel component that leads directlyto the unique capability for simultaneous recording, readout, or displayof the holograms is a 2-D source array 14, the light emission/reflectionfrom which must be coherent within each pixel but mutually incoherentamong all pixels. The array size will be determined by the array sizesof the SLMs employed in the architecture, as these will in fact delimitthe space-bandwidth product of all of the arrays. Given the geometricaland power dissipation constraints inherent in the preferred SLM designemployed herein, array sizes of ≈10⁴ to 10⁵ elements per cm² arecurrently appropriate. Given further the unique interconnectionrecording configuration proposed herein, larger array sizes can beconfigured by mosaic techniques, as the interconnection architectureautomatically compensates for irregularities in source location.

There are at least four possible structures that can satisfy thenecessary source array requirements, as described in a divisionalapplication of the grandparent application, "Incoherent/Coherent SourceArray for Multiplexed Holographic Recording and Readout", now issued asU.S. Pat. No. 5,339,177, (Au. 16, 1994). The first is an array ofoptically isolated surface-emitting semiconductor lasers, with adequatepixelation to eliminate the potential for inadvertent phase locking.

Let Δν be the processing-variation-induced or designed difference incenter frequencies from one source to the next. The mutual coherencetime between sources is determined by the optical bandwidth of thesources (in the case of such bandwidth being greater than Δν) or by Δν(in the case of Δν being greater than the individual source bandwidth).

For typical semiconductor lasers fabricated in the GaAs/AlGaAs system,for example, linewidths of 3 nm are common, which corresponds to afrequency bandwidth of approximately 1 THz. Over time scalescharacteristic of currently-available photorefractive volume holographicoptical interconnections, about 1 msec for power levels characteristicof semiconductor laser sources, this large bandwidth will assure mutualincoherence of the array elements. Total power dissipation assuming 1 mAthreshold laser diodes will be under 10 W/cm², and even then willrequire careful heat sinking and attention to thermal design. Theessential advantages of this approach are the anticipated very highresultant optical intensities of ≈5 W/cm² that will in turn acceleratethe holographic interconnection recording (and copying) process, and thesignificant technical leverage enjoyed by this approach due tosubstantial interest in semiconductor laser arrays for a wide range ofpotential applications.

For example, vertically emitting semiconductor laser arrays withdensities of over two million individual lasers per square centimeterhave been fabricated and evaluated successfully, as reported by J. L.Jewell et al, Optics News, pages 10-11 (December 1989). These arrays,however, have not been specifically designed to assure mutualincoherence among all of the individual source array elements, which isa critical feature utilized in the practice of this invention.

The second source array structure employs a pixelated piezoelectricmirror with an intentionally incorporated space-variant non-uniformity.The array is driven such that each individual high-Q mirror element isbrought into resonance at its natural (and distinct) center frequency.For such an array with 10⁴ elements, each separated by ≈2 kHz to satisfythe mutual incoherency requirements of the holographic interconnect, therequired bandwidth is only 20 MHz. This approach has the advantage ofpotentially very high reliability, with capability for reflectingessentially arbitrarily intense CW or pulsed source beams over a broadwavelength range.

The third source array structure is directly derived from the III-Vcompound semiconductor-based or other equivalent spatial lightmodulators discussed below. In this case, a pure phase modulatorgenerates the requisite frequency modulation to guaranteeelement-to-element mutual incoherence. Frequency separations aregenerated by replacing the detector/electronics combination associatedwith each pixel by an electronic ring oscillator or a stablemultivibrator with process-variable-induced spatial inhomogeneities inthe center frequencies across the array. The most demanding requirementfor this application is the necessity of achieving greater than π phasevariation with minimal associated amplitude modulation. This in turnwill require Δ(nd) products greater than 1/2 (optical path lengthdifferences given by either a change in the refractive index nmultiplied by the active device thickness d, or a change in devicethickness or displacement multiplied by the effective refractive indexof the active region, or both). Such Δ(nd) products may prove to bedifficult to achieve, for example, in traditional multiple quantum well(MQW) spatial light modulators based on the compound semi-conductorsystem, and may require the utilization of unusually large piezoelectriceffects in strained layer superlattices, or the incorporation of coupleddouble quantum wells (CDQWS) in modulation doped NIPI structures orplanar asymmetric Fabry-Perot cavities.

Implementation utilizing a wide variety of candidate spatial lightmodulator technologies such as liquid crystal light valves or deformablemembrane devices may prove particularly suitable for generation of thedegree of mutual incoherence required of the source array.

The fourth source array structure employs an acousto-optic deflector inconjunction with a prescribed electronic drive signal to generate a setof individually coherent but mutually incoherent beams derived from asingle laser source. In one such configuration, the electronic signalconsists of the coherent superposition of N waveforms with indices q=1through N, each shifted in frequency from the center frequency of theacousto-optic deflector by a given amount qΔν. This set of waveformswill produce a diffraction grating within the acousto-optic deflectorthat will (a) divide the incident beam into N+1 separate beams(including the undiffracted zero order beam), (b) shift the frequency ofeach individual beam by qΔν, and (c) deflect each beam through aseparate angle qΔθ. With appropriate imaging optics, this set of outputbeams can be used as a one-dimensional array of individually coherentbut mutually incoherent sources. Utilization of a second, orthogonallyoriented acousto-optic deflector cascaded with the first can produce atwo-dimensional array of such sources as well.

It will be noted that the fourth source array structure that utilizes asingle coherent input beam and one or more acousto-optic deflectors forarray generation has the advantage that only a single laser source isrequired; that the degree of coherence among all of the source beamsgenerated can be arbitrarily established (within limitations imposed bythe bandwidth of the acousto-optic deflector) by setting the frequencyshift induced between pairs of beams; that the incorporation of atunable laser as the single coherent source allows for broad flexibilityin establishing the central operating wavelength of the source array, asmay prove to be important in test applications for which the criticalwavelengths of other components within the architecture cannot bedetermined a priori; and that array nonuniformities can to a certainextent be compensated for (or desired array anisotropies generated) byadjustment of the analog driver signals used to generate each separatefrequency component, which in turn determine the diffractionefficiencies applicable to each individual source beam within the array.

3. Copying of Multiplexed Volume Holograms.

Also in accordance with the invention described in the grandparentapplication, apparatus is provided for copying an original multiplexedvolume hologram within a primary volume holographic optical element(master) to form an identical multiplexed volume hologram within asecondary volume holographic optical element (copy). The apparatus andmethod for copying a multiplexed volume hologram of planar objects thatare reconstructed as virtual images are described herein first, followedby a description of their generalization to multiplexed volume hologramsof planar amplitude objects, phase objects, 3-D objects, and multiplexedvolume holograms that reconstruct real images.

In the parent application of the present application, the use of thistype of apparatus and method for transferring information from anoriginal multiplexed volume holographic optical element into a secondaryvolume holographic (recording) medium, in which the information maygenerally be configured very differently than in the original hologram,is described. In addition, the application to two-way informationtransfer between two holographic media is provided. This application canbe used to lengthen retention time and to decrease or eliminate partialerasure during readout.

An embodiment of the copying apparatus is schematically depicted in FIG.7A and employs the original multiplexed volume holographic opticalelement 20 (master) to generate a substantially identical secondarymultiplexed volume hologram within a secondary volume holographicelement 120 (copy). An array 14 of coherent light sources that aremutually incoherent is employed, as described above. A beamsplitter 116is used to form two reference beams 113a, 113b, from each coherent lightsource 14a, 14b, etc., thereby forming two sets of angularly multiplexedreference beams, each set at a different location, but otherwisesubstantially identical. The first set of reference beams 113a isdirected onto the original multiplexed volume holographic opticalelement 20, such as by lens 42, to thereby form a set of output beams110'. The second set of reference beams 113b is directed onto asecondary holographic recording medium 120. In certain applicationspertinent to the invention, the two sets of reference beams may beeither wavelength multiplexed or spatially multiplexed or anycombination of angularly, spatially, and wavelength multiplexed.

Reference beams 113b are made to have phase fronts at recording medium120 that are substantially identical to the phase fronts of referencebeams 113a at holographic element 20. This can be provided, for example,by relay optics 44, 46, and 48. If lenses 44 and 46 each have focallength f_(r), then the optical distance from source array 14 to lens 44is f_(r), from 44 to 46 is 2f_(r), and from 46 to I₃ is f_(r), where I₃is an image of the source array. The optical distance from source array14 to holographic element 20 is equal to the optical distance from I₃ torecording medium 120. The position of lens 42 with respect toholographic element 20 is the same as the position of lens 48 withrespect to recording medium 120. Beamsplitter 116 and reflecting surface50 direct the reference beams 113 in the desired directions. Thus, theoptical path from beamsplitter 116 to holographic element 20 isessentially identical to that from mirror 50 to recording medium 120.

The set of reconstructed output beams 110' is directed from the originalmultiplexed volume holographic optical element 20 onto the secondaryholographic recording medium 120, such as by lenses 52, 54, with pathlengths sufficiently identical to the reference beam path lengths topermit coherent interference, pairwise, between the output beams and thesecond set of reference beams, inside the secondary holographicrecording medium.

In FIG. 7A, plane I₁ corresponds to the virtual image plane of theobjects, obtained from the reconstructed beams of the holograms recordedin holographic element 20. (Extensions to non-planar objects are givenbelow.) The images in I₁ can be completely overlapping (as in the caseof FIGS. 6A and 6B), partially overlapping, or non-overlapping in space(as in the case of FIGS. 4 and 5).

Lenses 52 and 54, of focal length f, are chosen to create an image ofplane I₁ at plane I₂. In this embodiment, plane I₁ is chosen to becoincident with the virtual image plane of the hologram. Plane I₁ existsat a distance Z₀ from the entrance face of the holographic element 20,and the image plane I₂ of I₁ exists at the same distance Z₀ from theentrance face of the holographic recording medium 120.

Due to the geometry of relay optics 52 and 54, the beams from I₂ areincident on recording medium 120 with phase fronts that aresubstantially identical to the original (primary) object beams that wereincident on holographic element 20, with the exception of an exactspatial inversion about the optical axis. (Such spatial inversion can beremoved, if desired, by inserting another f-2f-f optical relay system inpath 110', from I₂ to another real image plane I₂ '. The path of thereference beams 113b is similarly changed if needed to maintain therequisite pairwise coherence.) In the remainder of this section oncopying, the light distribution at I₂ that is subsequently incident onthe holographic recording medium will be referred to as if it were notspatially inverted, with the understanding that if a non-inverted copyis desired, the optics can be changed as described above, or changed toa three-lens amplitude-and-phase imaging system that has beendemonstrated experimentally in a multiplexed volume holographic elementcopying system (Sabino Piazzolla, B. Keith Jenkins, and Armand R.Tanguay, Jr., "Single step copying process for multiplexed volumeholograms," Optics Letters, Vol. 17, No. 9, pp. 676-678, May 1, 1992).

A set of holographic modulation patterns is then simultaneously recordedin the secondary holographic medium 120 by the interference of the setof output beams 110' with the second set of reference beams 113b,thereby forming the substantially identical multiplexed volume hologram.

Applications and extensions of this copying apparatus and method toother types of multiplexed holograms will now be discussed. First, allof the copying methods and apparatus described herein apply tomultiplexed holograms originally recorded simultaneously with an arrayof individually coherent but mutually incoherent sources, which resultsin a holographic record of an incoherent superposition of opticalinterference patterns in the master holographic medium; in this case,the copying apparatus reference beams 113a must approximate thereference beams 13a used during the original recording of holographicelement 20. In addition, these methods and apparatus also apply tosequentially recorded multiplexed volume holograms, since the netresulting holographic record within the master medium is an incoherentsuperposition of records of the same optical interference patterns. Hereagain, the copying can be made in one step, the requirement being thatthe set of reference beam phase fronts at holographic element 20 duringcopying approximate the set of reference beam phase fronts that wereused over time during recording of the original hologram.

Finally, these methods and apparatus can also be used to optically copycomputer-generated volume holograms. In this case, the resultinginterference pattern that is recorded in the secondary medium may byquite different than the pattern encoded into the master holographicelement; but the function of the copy hologram will be substantiallyidentical to that of the master. Examples of reasons for opticallycopying a computer-generated volume hologram include the reduction orelimination of unwanted spurious diffracted orders; an increase inoptical diffraction efficiency during readout; or the initialization ofinterconnection weights that were pre-computed and stored in a computergenerated hologram, then copied into a real-time optical medium that isused in an adaptive photonic neural network for subsequent informationprocessing.

The same holographic recording apparatus and method described above canbe used to copy multiplexed volume holograms of a set of planar phaseobjects that were recorded, for example, using a phase modulator atlocation 28 of FIG. 6A. This is possible because the imaging optics 52and 54 in effect copy not only intensity information but also phaseinformation from I₁ to I₂. This further permits generalizations tomultiplexed volume holograms of 3-D objects (again, of a set of originalstored holograms that was simultaneously or sequentially recorded),wherein the phase fronts from I₁ have been relayed to I₂ (or I₂ ' in thenon-inverted case). In this case, the plane I₁ represents the intensityand phase information of each beam propagating from each of the original3-D objects.

This apparatus and method can be extended to allow for copying ofholograms that reconstruct real images. Conceptually, in this case, theplane I₁ is located a distance Z₀ after holographic element 20, and thesubsequent relay optics 52, 54 are positioned the same, relative to I₁,as in FIG. 7A. Similarly, I₂ (or I₂ ') is positioned the same, withrespect to recording medium 120, as I₁ is positioned with respect toholographic element 20.

It should be noted that Z₀ does not have to be chosen exactly asdescribed above; in fact, depending on aberrations and apodizationeffects, Z₀ can, in many cases, be set equal to 0 (so that in the caseof planar objects, for example, I₁ is not coincident with the virtualimage plane of the recorded objects).

The copying apparatus can also be applied to reflection holograms. Byusing variants of the embodiment shown in FIG. 7A, for example, one cancopy from a multiplexed reflection holographic element to make anothermultiplexed reflection holographic element, as well as from a reflectionelement to a transmission element and from a transmission element to areflection element. Finally, multiplexed holographic elements that are ahybrid, in that they include some transmission holograms and somereflection holograms, can also be copied with a similar apparatus. Thesecases are described in more detail below.

FIGS. 7B-E show examples of embodiments of the copying apparatus forthese different cases of reflection and transmission holograms. In thesefigures, beam shaping optics such as lenses have been omitted forclarity. As described elsewhere in this section, any of a variety ofoptical imaging systems can be used in the reference and object beampaths for nearly identical copies, and other optical systems can be usedfor more general information transfer systems (described below).

FIG. 7B shows an embodiment for the case of transferring informationfrom a primary multiplexed volume holographic element 20' thatreconstructs in reflection, to a secondary holographic medium 120' thatwill, after recording, yield a secondary multiplexed volume holographicelement that also reconstructs in reflection. Beamsplitter means 43 andmirror 41 direct the two sets of reference beams to the two holographicmedia, and the reconstructed beams 110a interfere with the referencebeam 113d in the secondary medium 120' in a geometry suitable forrecording reflection multiplexed holograms. Of course, as in all copyingor information transfer geometries, the path lengths are keptsufficiently equal to ensure pairwise coherence in the secondary medium120'. The coherence length of the source will determine how close thepath lengths need to be. All of FIGS. 7B-F are drawn to depict that thepath lengths can be made to be substantially identical; optical sourceswith sufficiently long coherence lengths, however, permit relaxing ofthis constraint in the optical system. It will be clear to one skilledin the art that such longer coherence lengths can permit simplificationof the optical systems, by rearranging the optical components and beampaths.

FIG. 7C shows an embodiment for the case of transferring informationfrom a reflection primary holographic element 20' to a secondaryholographic medium 120 to form a transmission (secondary) holographicelement. Mirror 45 and beamsplitter means 43' direct the sets ofreference beams (113e and 133f) to the two holographic media, and 110bis the set of object beams that are output from the primary hologramduring reconstruction.

Similarly, FIG. 7D shows an embodiment for transferring information froma transmission primary holographic element 20 to a secondary holographicmedium 120' to form a form a reflection holographic element.Beamsplitter means 43" and mirrors 45' and 41' direct the two sets ofreference beams to the holographic media, and 110c represents the outputbeams being reconstructed from holographic element 20.

Finally, FIG. 7E shows an embodiment for transferring information from ahybrid transmission/reflection holographic element 20" to secondaryholographic medium 120" to form a secondary hybridreflection/transmission holographic element. Beamsplitter means 47, 49,and 149, and mirrors 53, 45", 51, 151, and 41" direct four sets ofreference beams to the two holographic media, in order to reconstruct(from 20") and record (in 120") both reflection and transmissionholograms. Beams 110_(d) represent the output beams being reconstructedfrom both reflection and transmission holograms in the primaryholographic element 20". In many cases a fixed mask element may be usedto send a particular subset of the set of reference beams generated bysource array 14 (those that correspond to transmission holograms) toholographic element 20" via beam path 113m, and a different subset ofthe reference beams (those that correspond to reflection holograms) toholographic element 20" via beam path 113n. Similarly, a mask element orspatial light modulator may be used in the beam paths (113k, 133p, 113q)that send reference beams to the secondary holographic medium to selectbeams for reflection and transmission holograms. Finally, it will benoted that the previous cases depicted by FIGS. 7A-D are included in theembodiment of FIG. 7E, as can be seen by blocking orremoving-appropriate beam paths in FIG. 7E.

Similarly, a variety of copying geometries are possible for eitherreflection or transmission holographic elements. For example, inaddition to straightforward geometries, the undiffracted order fromeither of the holographic elements can in some cases be used as the setof reference beams for the other (instead of using a beamsplitter togenerate two sets of reference beams). In this case, the reference beamscan be made to be substantially identical at the copy and at the master,if desired, by using an amplitude-and-phase imaging system with passiveoptical elements (such as lenses), or by using phase conjugationtechniques. A review of optical phase conjugation can be found inOptical Phase Conjugation, Robert A. Fisher, Academic Press, New York(1983).

By incorporating independent control of the sources in the source array,subsets of the original multiplexed volume holograms stored inholographic element 20 can be copied onto recording medium 120. This isuseful, for example, in a manufacturing environment in which differentcopies are meant to have different holographic recordings, each a subsetof the set of holographic recordings encoded in a master, completemultiplexed hologram. The sources in array 14 that correspond to thedesired holograms to be copied are turned on, and the others are leftoff. Alternatively, a spatial light modulator can be employed inconjunction with a lens to modulate an image plane of the source array14, in order to provide independent source control. Independent controlof the sources can also be used to partially or completely sequence thecopying process, so that during each exposure of a sequence of exposuresin time, a subset of the holograms is copied.

This functionality (that of independent source control) is also usefulin the cases of interconnection networks and neural networks, in which aportion of the master hologram is to be copied, to be later used torefresh that part of the original hologram. Alternatively, the copy canbe used as the interconnection hologram, and the master as a library ofinterconnection patterns, subsets of which are loaded into the copy 120to implement a desired interconnection.

At this point it should be clear to one skilled in the art thatholograms that are not stored in the master holographic element can beadditionally recorded in the copy medium during the copying procedure.This can be achieved by incorporating more than one master holographicelement, or by generating additional optical beams to make "original"holograms to be included in the secondary (copy) medium along with thosethat are copied from the master hologram.

Similarly, it should be clear to one skilled in the art that multiplecopies can be made using one apparatus, and for example even in a singleexposure step, by utilizing more than one secondary holographic medium.Two techniques can be used for this. In the parallel recording case,referring to FIG. 7A for example, the set of reference beams 113 issplit into more than 2 paths (a path being directed to each secondarymedium), and the set of output beams 110' is split into multiple paths,one being directed to each secondary medium. In the series recordingcase, the output beams 110' are sent to the first secondary medium, andthe undiffracted and unabsorbed component continues out the other sideof the secondary medium. It is then directed (with similar imagingoptics as between the primary and first secondary media) to the secondsecondary medium, and interferes with reference beams that were splitoff of 113b using a beamsplitter in place of mirror 50, for example; oralternatively, by using undiffracted reference beams transmitted by theprimary or first secondary medium. The copying apparatus cascades thesestages to provide copying onto additional secondary media. This seriescase enables more efficient utilization of the available optical powerthan does the parallel case.

Additionally, the entire multiplexed holographic element can berefreshed using the copying apparatus (or the information transferapparatus described below). If we copy back and forth between twoholographic media, we in effect have a resonator type structure if thecopying in both directions is performed simultaneously and continuouslyin time. This approach differs from other previous work (see, forexample, D. Z. Anderson, "Coherent optical eigenstate memory", OpticsLetters, Vol. 11, No. 1, pp. 56-58, January 1986) in that multipleholograms are being copied (refreshed) simultaneously, enabling a muchhigher storage capacity within the resonator apparatus. Note also thatwith this apparatus the two holographic elements need not be identicalcopies of each other at all, but could be quite different. A variety ofphysical arrangements can be used for this apparatus, and they are basedon the same underlying mechanisms as the copying and informationtransfer apparatus described in this section. One embodiment of such aresonator structure is shown in FIG. 7F, for the case of transmissionholographic elements. Source array 14, beamsplitter means 116, referencebeams 113a and 113b, mirror 50, and output reconstructed beam path 110eform a system that is substantially the same as the copying system ofFIG. 7A, operates using the same principles, and transfers informationfrom multiplexed volume holographic element 20 to holographic medium 120along beam path 110e. A similar arrangement is used to copy theresulting holographic modulation pattern in medium 120 to theholographic element 20 (also along beam path 110e), where it is recordedand reinforces the holographic modulation pattern within the holographicelement 20. Reference beams are provided for this return path transferby phase conjugate mirrors 55 and 55', which phase conjugate theundiffracted zero orders (i.e., transmitted reference beams) of the twoholographic elements. Again, path lengths are adjusted to ensurepairwise mutual coherence between each phase conjugated reference beamcoming along beam path 213a, and each object beam coming along beam path110e, at the medium of holographic element 20.

While it is clear that a real-time holographic material is foreseen foruse as the copy holographic medium in some of the above-mentionedapplications, the previous resonator example shows that in some cases itis also desirable to use a real-time material for the master holographicmedium. Another example that utilizes this capability is describedbelow.

The similarity between two multiplexed holographic elements can bemeasured by using the copying apparatus in the forward or reversedirections. For example, the output beams recalled from one multiplexedholographic element, when incident in the object beam directions on asecond multiplexed holographic element, can recall a set of referencebeams. The nature (e.g., intensity) of the recalled reference beamsprovides information on the similarity (e.g., correlation) between eachpair of corresponding holograms of the two multiplexed holographicelements. Then, as new holograms are loaded into the first (master)multiplexed holographic element, they can be correlated with those inthe secondary-medium. Note that this process can correlate, pairwise, alarge number of 2-D images simultaneously. In the particular case of thefirst multiplexed holographic element being a copy of the secondmultiplexed holographic element, this procedure can provide ameasurement of the fidelity of the copy.

Finally, it will be appreciated that the apparatus and method can alsobe used to make non-identical copies, in which there is magnification ofthe spatial extent of the stored images by incorporating opticalmagnification into the path 110' (or magnification of angles byincorporating optical demagnification into path 110'). Alternatively,the reference beam illumination of the copy 120 can be changed relativeto the original by changing the phase fronts incident on the copy. Thisis needed for applications in which a set of hard-to-generate storedpatterns are to be transferred from a master multiplexed hologram to acopy, but the copy is to be used in an optical system that utilizes adifferent set of reference beams to recall the stored holographicimages. In this case, the optics in path 113b are chosen to make thephase fronts incident on recording medium 120 substantially identical tothe desired new reference beam phase fronts that will be used toreconstruct the copy. In these non-identical copying cases, the newoptics must be chosen so that the optical path length constraint betweenreference beams and object beams, pairwise, is still satisfied, toassure interference between the mutually coherent beams pairs.

Another example of changing the reference beam formats for the copyholographic element is in cryptography. Each reference beam can carry aspatial code that must be used (as a key) to recall each hologram. Inthis case, spatial modulation is encoded onto each reference beam. Aslight variant is to use the object beams as the keys, so the copyhologram is recalled by using incident object beams, thus generating oneor more reference beams as output(s).

More generally, an extension of the non-identical copy concept is the"transfer of information" from one multiplexed holographic element to asecondary holographic medium. For example, the secondary medium can bein the Fresnel or Fraunhofer regime of the master. Thus, the upper path110' of FIG. 7A is configured differently, and in some cases does noteven require any lenses. Uses of this information transfer mechanisminclude, for example, producing a holographic optical element. Themaster holographic element can be exposed in one optical location, butits "copy", which is to be used in a final optical system, may besituated in a different optical location (e.g., "upstream" or"downstream" of the master holographic element's location). Another useof this information transfer mechanism is in the two-holographic-elementfeedback resonator arrangement described above, in which the twoholograms are not disposed in a conjugate amplitude-and-phase imagerelationship to each other; a unique feature of such a geometry is inthe effect of nonlinearities in the recording and reconstructionprocess. The nonlinearities of one holographic element can be used toadvantage, e.g. for nonlinear information processing functionality, orfor thresholding to provide noise removal and signal level regeneration.The nonlinearities of the other holographic element can at the same timebe minimized, e.g. by using a lower overall diffraction efficiency.

A furtherance of the capability to make non-identical copies is that ofwavelength conversion, in which the recording wavelength generated bythe source array is not the same as the wavelength to be utilized inreconstruction. This feature is particularly useful in the case ofcurrently-available photorefractive volume holographic recordingmaterials, which can be non-destructively read out (reconstructed) onlyat a wavelength of relative photorefractive insensitivity. In certaincases, the Bragg condition can be satisfied by altering the scale of thesource array used for copying in comparison with the scale of the sourcearray used for subsequent reconstruction, and by reconfiguring theoptics between the source array and the holographic recording medium.

4. Comparison of Architecture of the Invention with PreviousApproaches--Simulation Results.

FIG. 8 schematically illustrates what would happen in the case of usingthe sets of object and reference beams 11, 13, respectively, in an N:Nfan-out/fan-in case, of which a 3:3 fan-out/fan-in case is shownexplicitly. The beams 13 comprise the three reference beams x₁, x₂, andx₃ (shown explicitly), among others (indicated by the set of threedots). Object beams 11 comprise y₁, y₂, and y₃ (shown explicitly), amongothers. It is desired to record a fully connected interconnectionpattern, with an independent interconnection weight established betweeneach "input" x_(j) and each "output" y_(i). In FIG. 8, dashed linesindicate the presence of beams employed at some point during therecording cycle, while solid lines indicate a specific readout examplein which only the beam x₁ is used as an input, generating the zerothorder beams x₁ ', x₂ ', and x₃ ', as well as the output (reconstructed)beams y₁ ', y₂ ', and y₃ '. As will be shown in FIGS. 9 and 10, such anarrangement, typical of the interconnection schemes investigated in theprior art, is subject to a throughput loss (optical inefficiency) ofsignificant magnitude when each common object beam such as y₁, y₂, or y₃is utilized to record either simultaneous (coherent or incoherent) orsequential (incoherent) interconnections with either a full or partialset of reference beams x₁, x₂, and X₃, and the readout is performed withmutually incoherent reference beams. In this case, readout with two ormore reference beams creates equally many beams propagating in eachoutput direction y_(i) '. Such output beam directions for any givenoutput beam y_(i) ' are hence degenerate, and the throughput loss is infact directly attributable to this beam degeneracy. Throughput losseswill also be observed when the readout is performed with mutuallycoherent reference beams if the recording process was performed eithersimultaneously with mutually incoherent reference beams, or sequentiallywith independent reference beams. Furthermore, these interconnectionschemes are subject to both a significant throughput loss and coherentrecording crosstalk when the same sets of interconnections are recordedsimultaneously with mutually coherent sets of reference and object beams(such as y₁ with x₁, x₂, and x₃).

In the discussion of phase volume holographic recording, a quantity ofimportance is the strength v of a given recorded holographic grating,which is defined as

    v=(2π/λ)Δn d

in which λ is the wavelength utilized for holographic gratingreconstruction, d is the effective thickness of the holographicrecording medium, and Δn is the amplitude of the modulated index ofrefraction associated with this given grating, such that the spatialdependence of the local index of refraction on the spatial coordinate xis given by:

    n(x)=Δn sin (2πx/λ).

In the case of either incoherent or coherent (sequential) recording withincoherent readout of the interconnection gratings, fan-in throughputloss is observed. In this example, the weights are in the ratio of 1:2:3(w₁₁ :w₂₁ :w₃₁). In addition, the remaining interconnection weights havebeen recorded such that w_(1j) :w_(2j) :w_(3j) are also in the ratio1:2:3 for j=2,3 and w₁₁ =w₂₂ =w₃₃.

The results of simulations utilizing the optical beam propagation methodare given in FIG. 9, which shows that the ratio of the fan-out (here,1:2:3) is retained; however, the total efficiency (0.06+0.09+0.18) isconsiderably less than 1, due to the throughput loss from thetransmitted zeroth order beams 210' (a direct result of beamdegeneracy). This can be simply explained by reference to FIG. 8, fromwhich it can be inferred that reconstruction beams 10' comprisingoutputs y₁ ', y₂ ', and y₃ ' are automatically Bragg matched to theinterconnections recorded between x₂ and y₁, y₂, and y₃ and between x₃and y₁, y₂, and y₃. Hence, y₁ ', y₂ ', and y₃ ' reconstruct unwanted (inthis example) zeroth order beams 210' comprising x₂ ' and x₃ ', whichtake considerable efficiency from the reconstruction of y₁ ', y₂ ', andy₃ '.

In the case of coherent and simultaneous recording of theinterconnection gratings, not only is fan-in throughput loss observed,but also coherent recording-induced crosstalk is seen. In FIG. 10, thetotal efficiency is, like in FIG. 9, considerably less than 1, due tothe beam degeneracy throughput loss. Further, the correct ratio of thefan-out is lost at and near the peak diffraction efficiency, due torecording-induced crosstalk. The notion of maintaining efficientinterconnections in such an arrangement is thus seen to be a myth.

FIG. 11 is similar to that of FIG. 8, except that it is based onemploying the architecture of the invention, and shows the angularmultiplexing of both the object (source) and reference beam sets 11, 13,respectively, as well as angular multiplexing of the fan-in to a givenoutput node. In FIG. 11, coherent pairs of object beams 11 and referencebeams 13 are depicted in like manner; since all of the reference beamsare mutually incoherent due to the source array 14 (as shown, forexample, in FIG. 6A), each reference beam x_(j) interferes with only onegiven object beam passing through the point y₁ ; therefore, none of thereconstructed beams 10' and zeroth order beams 210' are Bragg-matched toadditional gratings and hence no beam degeneracy throughput loss isobserved.

It will be noted with reference to FIG. 11 that imaging optics (notshown) can be used to combine image-bearing beams incident at differentangles and superimpose them in a plane so that they are in registry on apixel-by-pixel basis. This superposition function is enabled by therecording geometry described in FIG. 6A, in that all individuallycoherent but mutually incoherent object beams pass through spatial lightmodulator 28, each at a separate angle.

Coherent recording-induced crosstalk is eliminated among the referencebeams, since they are all mutually incoherent. Coherentrecording-induced crosstalk among the object beams is limited again bythe mutual incoherence of the source-derived beams to occur only amongthe set of object pixels illuminated by each coherent and expandedobject beam. This latter source of crosstalk can be reduced either byincreasing the intensity of the set of reference beams relative to theintensity of the set of object beams, or by utilizing the subhologramversion of the architecture (which achieves crosstalk reduction byspatial segregation).

In FIG. 11, an incoherent fan-in due to output point y₁ ' is shown toconsist of a weighted sum of inputs of the form w₁₁ x₁ +w₁₂ x₂ +w₁₃ x₃=y₁, or, in general for an N-input, N-output fully connectedinterconnection network: ##EQU1##

The representation used for drawing the vector directions and scales ofthe input and output beams in FIG. 11 presumes an asymmetric input andoutput lens configuration (meaning that the input and output lenses,which are not shown, have different focal lengths). (Such an asymmetricinput and output lens configuration is depicted in FIGS. 6A (lens 26)and 6B (lens 38)).

5. Modulation and Spatial Light Modulators.

As is well known to those skilled in the art, the modulation, orequivalently optical modulation, of an optical beam or a set of opticalbeams involves the modification by some controlling means of theamplitude, or phase, or both amplitude and phase of the optical beam orbeams. As is equally well known to those skilled in the art,space-variant modulation of the amplitude of an optical beam (as opposedto uniform modulation of the amplitude of an optical beam) can beimplemented in such a manner as to provide convergence (focusing) ordivergence (defocusing). Simultaneous modulation of a set of opticalbeams effects the same modification on all of the optical beams withinthe given set, whereas independent modulation effects separatelycontrollable modifications of each separate optical beam within the setof beams.

In order to effect controllable modification of an optical beam or setof beams, and hence to controllably modulate the set of optical beams,means for modulation must be employed that comprise separate detection,functional transformation, and modulation functions. The detectionfunction may comprise either electrical detection of a control signal,or optical detection of an input control beam. The functionaltransformation may be represented in analog, digital, or hybridanalog/digital form, and may implement a wide array of functions,depending on the application at hand, including (but not limited to)linear transformations, nonlinear transformations, amplification,thresholding, level restoring, saturation, and specific algorithmicdependencies.

In some cases, controllable modification of an optical beam or set ofbeams can be effected by direct modulation of one or more of a set ofoptical sources. For example, in the invention that is the subject ofthe present application, independent control of the output amplitude orintensity of each individually coherent source within thetwo-dimensional mutually incoherent source array can be accomplished bydirect electrical modulation of either the driving current or voltageapplied to each individual source. In this case, the electricalmodulation function can be either analog or digital (binary), and meansare provided for separate connection to each individual source by eithermatrix addressing techniques or sequentially-addressed temporalmultiplexing techniques that are well known to those skilled in the art,for example, of liquid crystal displays. The incorporation of suchelectrical modulation capability within the architecture shown in FIG.6D, which depicts an embodiment of apparatus that is optimized forincoherent/coherent readout and display of double angularly multiplexedvolume holographic optical elements (without provision for recording),provides one means for independent control of each reference beamthrough modulation of the set of sources within the incoherent/coherentsource array.

Spatial light modulators comprise a broad class of optical devices thatincorporate these controllable modulation capabilities in the opticalrather than in the electrical domain. When spatial light modulators areused for this function, modifications are made to the optical beamsemitted by the incoherent/coherent source array, rather than bymodifying the electrical signal that drives each source elementdirectly. A wide variety of spatial light modulators have beeninvestigated for use in technological applications such as thosedescribed in the present application, based on a number of differenttechnical approaches. These technical approaches include, but are notlimited to, liquid crystal, electrooptic, acoustooptic, deformablemembrane, photorefractive, dichroic, electroabsorptive,electrorefractive, photochromic, quantum-confined Stark effect,Franz-Keldysh effect, multiple quantum well (MQW), coupled doublequantum well (CDQW), and magnetooptic modulation mechanisms. Thedetection process employed, by which means each individual pixel(picture element) of the spatial light modulator can be controlled, mayresult in an electrically addressable spatial light modulator, anoptically addressable spatial light modulator, or a hybrid combinationof the two principal address mechanisms.

In one embodiment of apparatus that is optimized for incoherent/coherentreadout and display of double angularly multiplexed volume holographicoptical elements (without provision for recording), as shownschematically in FIG. 6D, spatial light modulator 32 can be included toprovide for optical modulation of the set of reference beams derivedfrom the incoherent/coherent source array. As such, this spatial lightmodulator adds the feature of independent optical control of each of thebeams within the set of reference beams, and may be employed inconjunction with direct electrical control of the source array(discussed above) to provide additional degrees of freedom in thecontrol algorithm employed. In this case, a preferred embodiment for theSLM includes matrix electrical or optical addressability, a nonlineartransfer characteristic (such as a binary on/off characteristic), andtransmission-mode operation as shown schematically in FIG. 6D. Althoughthe goal of full monolithic integration of the detection, functionaltransformation, and modulation functions of a spatial light modulatorwithin a single technological substrate is ultimately preferred, hybridintegration of the detection and functional transformation functionswithin the silicon VLSI technology base, and of the modulation functionwithin either the liquid crystal or compound semiconductor technologybases (discussed in more detail below), in conjunction withreflection-mode operation, is currently envisioned.

As will be easily appreciated by those skilled in the art, the array oftechnological applications described herein requires an equally broadarray of SLM embodiments for incoherent/coherent readout and display ofdouble angularly multiplexed volume holographic optical elements, asdiscussed below in the context of each particular application (such asneural networks, optical information processing, optical memory, opticaldisplays, and holographic optical elements).

A similar array of possible SLM embodiments applies to spatial lightmodulators employed in architectures that implement the recordingfunction alone, or the recording function in addition to the readoutfunction. For example, such SLMs include SLM 28 as depicted in the upper(recording) arm of FIG. 14, and SLM 80 as depicted in the upper(recording) arm of FIG. 15. As above, the requirements for each of theseSLMs are application-dependent. In what follows, we provide a specificexample of such a preferred embodiment for the case of neural networkapplications.

The detection, amplification, functional implementation, and modulationfunctions required in both the neuron unit output and input planes forneural network application are envisioned to be incorporated inmultifunction spatial light modulators. A dual rail differentialapproach may be employed as it inherently incorporates considerablefunctional generality, with capacity to accommodate both bipolar inputsand bipolar outputs. The simpler case of unipolar outputs and bipolarinputs, also common in neural network models, represents a subset of ourfully bipolar design and requires even less chip area. The dual railapproach involves the hybrid or monolithic integration of two detectors,appropriate amplification and control circuity, and two modulatorswithin each SLM pixel, as shown in FIG. 12. A primary approach is todevelop analog circuitry that is process-compatible with both detectorand modulator requirements, and at the same time utilizes minimumintegrated circuit real estate. Although development of secondgeneration chips in the compound semiconductor system may utilize eithermultiple single-quantum-well or multiple coupled-double-quantum-wellmodulation and detection elements in conjunction with electronic circuitelements such as bipolar junction transistors, MESFETs, MISFETs, HEMTsor resonant tunnel diodes (RTDs), the first generation chips have beendesigned within the silicon repertoire (MOSIS (Metal Oxide SemiconductorImplementation Service, Information Sciences Institute, University ofSouthern California) design rules) in order to establish functionalintegrity and preliminary estimates of non-ideality and process-inducedvariances. Furthermore, hybrid integration of silicon chips (withintegrated detectors and control electronics) withcompound-semiconductor-based or other technological implementations ofthe modulation function can be accomplished by bump contact bonding inconjunction with appropriate through-substrate vias. Alternatively, thevias can be eliminated by the use of transparent modulator substrates,with the modulation elements operated in the reflection mode, inconjunction with a second-bump-contact-bonded substratehybrid-integrated with the first to provide the detection and controlcircuitry on the two innermost facing substrate surfaces. The currentchip set contains 100×100 μm pixels, within which 2500 μm² is dedicatedto dual rail circuitry that implements a linear transfer characteristicwith both upper and lower level saturation (FIG. 13), a function ofconsiderable utility in the neural network application, as described inmore detail in a succeeding section. The design described hereinincorporates only fifteen transistors per pixel within 2 μm minimumfeature size design rules, and allows for 10⁴ dual rail pixels/cm².

While any of a variety of SLMs may be used in the practice of theinvention, the SLM described below is preferred for neural networkapplications. The preferred SLM for representation of the neural unitinput and output planes is optically addressed (as opposed toelectrically addressed) and is depicted in FIG. 12. The SLM comprises asubstrate 56 comprising a plurality of pixels 58, at least two portionsof each pixel comprising regions 60 that can be controllably madetransparent to incident light with varying degrees of optical densityfrom a first source (such as source array 14). Means 62 are associatedwith each transparent region 60 to modulate the passage of lighttherethrough. Alternative means can be provided for modulation of thereflection of light from, rather than the passage of light through, eachseparate modulation element within each pixel.

Detector means 64 associated with each pixel detect incident light froma second source or set of second sources, such as from the output of themultiplexed storage holographic element 20; see, e.g., FIG. 14. Thedetector means generates an electrical signal, which is fed toelectronic means 66 associated with each pixel 58. The electronic means66 is responsive to the electrical signal from the detector andgenerates a modulation signal which is sent to the modulation means 62.The electronic means 66 comprises, therefore, the several functions ofelectrical signal transduction (following each detector), signalamplification and level shifting, transfer function implementation(establishment of the functional relationship between the inputopticalintensity and the output optical amplitude or intensity followingthe modulator element), and impedance matching to the electricallyactivated means of each modulation element. As a result, lighttransmitted through or reflected from the SLM is modulated according toan overall transfer function relationship that implements a desiredalgorithmic dependence, as specified further in the several followingsections.

Both ⊕ (positive) and ⊖ (negative) channels are depicted in FIG. 12.Note that both polarity channels are provided for each of the detectionand modulation functions within each individual pixel. In the preferredembodiment, this allows for the incorporation of both positive valuedand negative valued interconnection weights w_(ij), each carried as aseparate channel within each individual pixel. This arrangement may besummarized as allowing for the incorporation of both bipolar inputs andbipolar outputs within a given interconnection network.

In the preferred embodiment, the electronic means 66 is utilized in amodified differential amplifier configuration, which is designed suchthat the ⊕ modulator is driven to increasing transmissivity (orreflectivity) when the ⊕ detector output exceeds the ⊖ detector output;conversely, the ⊖ modulator is driven to increasing transmissivity (orreflectivity) when the ⊖ detector exceeds the ⊕ detector output.Additionally the ⊕ modulator is not driven when the detector outputdifference (⊕-⊖) is negative, and the ⊖ modulator is not driven on whenthe detector output difference is positive, as shown in FIG. 13.

Four additional novel spatial light modulator configurations are a partof the invention described in the grandparent and applications, nowissued as U.S. Pat. Nos. 5,121,231 and 5,416,616, respectively. In thefirst, the control circuitry is designed to implement either an a stablemultivibrator or ring oscillator, with either design-induced orprocess-variable-induced variance across the pixelated array in thecenter resonant frequency of the resultant oscillation, in such a mannerthat the individual pixels temporally modulate fully coherent lightproducing a mutually incoherent set of modulated beams. Such a spatiallight modulator configuration is one preferred embodiment for the sourcearray device described above.

In the second configuration, local interconnections among nearestneighbor or next-nearest-neighbor pixels are incorporated such that thecontrol circuitry drives the modulation elements in a manner thatdepends not only on the one or more optical inputs to a given pixel, butalso on either the one or more optical inputs to neighboring pixels, oron some functional derivative thereof as determined by control circuitryin each pixel.

In the third configuration, the modulation elements are designed inconjunction with a transparent substrate, or in the case of a hybridintegrated device with two transparent nonidentical substrates, suchthat the modulation creates a variable reflectivity and a variabletransmissivity in each pixel, the one being the complement of the otherin order to satisfy conservation of energy laws. In this case, both thearray of reflected beams and the array of transmitted beams as somodulated constitute separate signals to be utilized in theimplementation of system functionality.

In the fourth configuration, two superimposed optical modulationelements are incorporated in each pixel, one vertically above the otheras referenced to the substrate plane, such that each is independentlycontrollable by means of the incorporated control circuity (in turndependent on the electrical and/or optical input state(s) of eachpixel), with one of these elements exhibiting principally phasemodulation in response to its input variable, while the other of theseelements exhibits principally amplitude modulation in response to itsindependent input variable. In this manner, independent control of boththe amplitude and phase modulation exhibited by each pixel isachievable; in addition, compensation can be provided for undesirablemodulation-dependent phase in an amplitude modulation application,and-the compensation of undesirable modulation-dependent amplitude in aphase modulation application.

It should also be noted that another way of achieving both amplitude andphase modulation is by means of a hologram. A planar or volumeholographic optical element can provide spatial modulation of a beam orset of beams, either static modulation by using fixed materials ordynamic modulation by using real-time materials. Of course,interconnection functionality can also be incorporated into the sameholographic optical element.

6. Holographic Recording Media.

A wide variety of volume holographic recording media may be employed inthe practice of the invention, including static (fixed) media such asphotographic film, dichromated gelatin, layered thin film media, andcertain photopolymers, as well as dynamic (real time) media such asphotorefractive refractory oxide single crystals (e.g., bismuth siliconoxide, bismuth germanium oxide, bismuth titanium oxide, barium titanate,potassium tantalate niobate, strontium barium niobate, potassiumniobate, lithium niobate, and lithium tantalate), photorefractivecompound semiconductor single crystals (e.g., chromium-doped galliumarsenide, intrinsic (undoped) gallium arsenide, cadmium telluride, andiron-doped indium phosphide), photochromic glasses, andbiologically-derived photosensitive molecules dispersed in variousmatrices.

In each case, it is desirable for purposes of scalability in thepractice of the invention that such materials be configured so as toexhibit "thick" holographic grating characteristics, as defined by thewell-known holographic parameter Q defined by

    Q=2πλd/nΛ.sup.2

in which both λ and d have been previously defined, n is the average(unmodulated)-index of refraction of the holographic recording medium,and Λ is the period of a given recorded grating. Thick holographicgrating performance is usually observed when the recordingconfigurational parameters are so chosen or constructed that Q≧10. Forsuch values of Q, the Bragg width (angular response characteristicsabout the Bragg angle) given by ⊖_(B) =arcsin(λ/2Λ) can be made narrowenough to support a large number of independent gratings capable ofreconstruction without interference, overlap, or interchannel crosstalk.

Although most "thick" volume holographic media investigated to datecomprise a uniform photosensitive material, an additional type of volumeholographic media is applicable for use in conjunction with theteachings of the invention. In these so-called stratified volumeholographic optical elements (R. V. Johnson and A. R. Tanguay, Jr.,"Stratified Volume Holographic Optical Elements", Optics Letters, Vol.13, No. 3, pp. 189-191, 1988), thin layers of photosensitive materialare separated by buffer layers of non-photosensitive materials to form amultilayer structure. Volume holographic optical elements can be formedin these stratified media by standard optical recording techniques; inparticular, the optical recording apparatus and recording methods thatare part of this invention can be used. Such stratified volumeholographic optical elements exhibit a range of novel diffractionproperties such as periodic peaks in the angular dependence of thediffraction efficiency, wavelength notch filtering, and spatialfrequency notch filtering, in addition to the emulation of manyessential features of thick volume holographic media.

Computer generated holograms comprise holographic modulation patternsthat are calculated to achieve specific diffraction properties. Suchcomputer generated holograms can be fabricated by optical recording(usually with a scanning laser beam) in thin photosensitive mediasupported by a substrate, by electron beam photolithographic techniquesin electron-beam sensitive media, or by optical photolithographictechniques-in conjunction with an appropriate mask containing thecomputer-generated pattern. As is well appreciated by those skilled inthe art of volume holographic recording and readout, because theseholographic modulation patterns are typically calculated by computer andfabricated using one or more of these computer-driven techniques, theresulting holographic modulation pattern is usually quantized in one ormore of the available material modulation parameters, or issubstantially discrete (as opposed to continuous with smooth gradients)in one or more spatial dimensions, or both.

The concept of stratified volume holographic optical elements can befurther extended to include multilayer computer generated holograms, inwhich a multilayer stack of appropriately designed computer generatedholograms is assembled (with attention to careful alignment) to form athick volume holographic medium with volume diffraction properties. Asis well known to those skilled in the art, while the resulting volumeholographic modulation pattern can be considered to be spatiallydiscrete in the dimension that crosses the layers of such computergenerated holograms, for reasons described above, the computer-generatednature of the patterns can also yield a substantially discrete (asopposed to continuous with smooth gradients) pattern of modulation inone of the other two (transverse) dimensions (within the layers of suchcomputer generated holograms). In certain cases, it may proveadvantageous to form a limiting case of a computer-generated stratifiedvolume holographic optical element in which the buffer layers areeliminated entirely to form a contiguous multilayer structure.

It will be obvious to those skilled in the art that holographicmodulation patterns can be stored as modulations in microscopic materialparameters, such as index of refraction and absorption coefficient ofthe holographic medium. It is also well known that holographicmodulation patterns can be described as modulations of more macroscopicmaterial parameters, such as optical path length, transmittance, andreflectance within the holographic medium. These macroscopic parametersare often convenient for the case of computer-generated structures, suchas those described above.

B. NEURAL NETWORKS

1. Technical Approach.

The basic elements and functions of common neural networks are discussedabove and shown in FIGS. 1-3. A neural network typically learns bychanging its interconnection weights according to a learning technique,which is typically expressed as an update rule for the weights. Afterthe network has learned, the values of the interconnection weights maynot be known (and may be difficult to probe); only the correctperformance of the overall neural network is verified.

A general neural network architecture should have the followingfeatures: (1) modularity, i.e., be in the form of a cascadable "module";(2) capability for lateral, feedforward, and feedback interconnections;(3) analog weighted interconnections; (4) bipolar signals and weights;(5) scalability to large numbers of neuron units with high connectivity;(6) capability for single-step-copying of a learned (weighted)interconnection pattern; and (7) generalizability to different networkmodels and learning algorithms, as well as capability for extension topossible future network models.

Recently, there has-been a substantial amount of research anddevelopment on optical and optoelectronic implementations of neuralnetworks; to the best of the inventors, knowledge, none of the opticalor optoelectronic systems described to date by others havesimultaneously demonstrated all of the foregoing features. The apparatusdescribed in the parent application as well as herein, as applied toneural networks in the given embodiments, provides for essentially allof the above features.

This architecture utilizes the novel incoherent/coherent hologramrecording and reconstruction apparatus of the invention, and has angularmultiplexing at each input node, configured to produce angularmultiplexing of the fan-in to a given output node. This provides forsimultaneous read/write capability with reduced crosstalk and enhancedoptical throughput. The use of this apparatus with multiplexed volumeholograms permits scalability of the neural network and itsinterconnections. It also provides simultaneous updates of all weightsat each iteration of learning. Since some learning techniques (e.g.,multilayer supervised learning) can require an extremely large number ofiterations for large networks, fast weight updating is crucial. Inaddition, since the copying apparatus described in an earlier section(above) can be used directly in neural network applications, rapidcopying of all recorded weighted interconnections can be readilyperformed. Thus, duplicates of the weighted interconnections within aneural network that has learned a given processing function can berapidly manufactured.

Optoelectronic spatial light modulators with hybrid or monolithicallyintegrated detectors, modulators, and electronics at each pixel asdescribed in the previous section are envisioned for the 2-D neuron unitarrays. These spatial light modulators provide for flexible functionswithin a single technology, thus enabling generalizability to differentneural network models and learning algorithms. They also permit bipolarsignals and synaptic weights to be integrated into the systemarchitecture.

The use of photonic technology provides for high fan-in/fan-outcapability via optics as well as parallel input/output for incorporationinto larger heterogeneous or homogeneous systems without loss of systemthroughput, thus providing modularity. The photonic architecturescomprising preferred embodiments of the present invention and its parentreadily generalize to many neural network models (including single andmultilayer, feedforward and recurrent networks) and learning algorithms(supervised and unsupervised), with applications to associative memory,combinatorial optimization, and pattern recognition, including visionand speech.

2. Interconnections.

For the purposes of the present discussion, consider the connectionsfrom a single neuron unit, including fan-out and synaptic weights, to berepresented by a single hologram. During learning, all holograms areupdated simultaneously in a photorefractive crystal or other suitablevolume holographic recording medium. This is done by using oneself-coherent beam pair for each recorded hologram, in theincoherent/coherent, angularly multiplexed fan-in apparatus and methoddescribed earlier (e.g., FIG. 6A). Referring to FIG. 6A, the set ofreference beam intensities x_(j) serves as the set of input signals tothe neural interconnections, and the set of signals A_(j) serves as theset of training signals during learning. The holograms are thenreconstructed by the same set of reference beams, as shown in FIG. 6B.This results in the desired incoherent sum Σ_(j) w_(ij) x_(j) at eachpixel of the output array, in which w_(ij) is the stored interconnectionweight from neuron unit j to neuron unit i.

Experimental results on writing and reading angularly multiplexed volumeholograms using this incoherent/coherent process in silver halide andphotorefractive bismuth silicon oxide media show minimal crosstalk atthe same time as high optical throughput.

The advantages of this technique are as follows:

(1) All weights can be updated simultaneously. This obviates the needfor sequential exposures which are inefficient as well as timeconsuming, and at the same time maximizes parallelism.

(2) Both the object beams and the reference beams are angularlymultiplexed, and each training signal pixel as well as each output nodecorresponds to a set of angularly multiplexed beams. This latter featurealone is unique to the present invention and its parent. This angularmultiplexing technique circumvents the problem of incoherent fan-inloss, maximizing optical throughput, providing incoherent pixel-by-pixelsummation, and minimizing beam degeneracy crosstalk. (In addition,crosstalk due to accidental grating degeneracies is eliminated byoptimization of the geometry of the beams, as well as by the spatiallight modulator placement and pixelation; see, e.g., D. Psaltis et al,Proc. SPIE, Vol. 963, pp. 70-76 (1988).)

(3) As described above, this technique permits the capability of rapidlycopying the entire collection of recorded interconnections and weightsto another volume holographic medium by using this sameincoherent/coherent reconstructing and recording technique. In additionto that described above, another advantage of this technique is thecapability to refresh the interconnection periodically, by copying itback and forth between two or more holographic media; additionally, twoparallel networks can be implemented to separate the learning functionfrom the processing function. The architecture described in the parentapplication is unique to the best of the inventors' knowledge inallowing for this possibility.

In order to adaptively interconnect a large number (10⁴ to 10⁶) of inputelements to an equally large number of output elements with highconnectivity and negligible crosstalk, the most attractive candidatetechnology is currently that of photorefractive volume holographicoptical elements. For many (if not all) proposed optical implementationsof neural networks, including that described herein, demonstration ofappropriate degrees of reconfigurable multiplexing capacity withnegligible or at least tolerable interconnection crosstalk is essentialto the achievement of successful integration. The architecture proposedherein is uniquely designed to accentuate the strengths of currentlyavailable photorefractive materials (such as Bi₁₂ SiO₂₀ and GaAs), whileminimizing the inherent weaknesses. For example, the incorporation of afully parallel weight-update scheme with mutual incoherence betweenpairs of sources results in a significant reduction in the degree ofsource-generated crosstalk characteristic of fully coherent recordingschemes, while simultaneously obviating the need for sequentialrecording that is particularly cumbersome and time consuming inphotorefractive media.

3. Learning Techniques.

A broad class of learning techniques, both supervised and unsupervised,can be represented by the single weight update equation:

    Δw.sub.ij =αδ.sub.i x.sub.j -βw.sub.ij(1)

in which Δw_(ij) =w_(ij) (k+1)-w_(ij) (k) is the weight update, x_(j) isthe signal level of the j^(th) input (e.g., j^(th) neuron unit of theprevious layer in a multilayer network), and δ_(i) is dependent on theparticular learning technique. In Eqn. (1) above, α>0 is required andβ≧0 is dictated by the physical constraints of the material (assuming norefreshing with gain greater than or equal to unity). The architecturesdescribed herein implement learning of the form of Eqn. (1). Specificexamples include:

    δ.sub.i =y.sub.i (Hebbian)

    δ.sub.i =t.sub.i -p.sub.i (Widrow-Hoff)

    δ.sub.i,l-1 =f'(p.sub.i,l-1)Σ.sub.k δ.sub.k,l w.sub.ki

(Back propagation, all layers except output layer)

    δ.sup.i,L =(t.sub.i,L -y.sub.i,L)f'(p.sub.i,L)

(Back propagation, output layer; least mean square (LMS), single layer)

in which y_(i) denotes the output of neuron unit i in the current layer,t_(i) is the target or desired value for the output of neuron unit i forsupervised learning, δ_(i),l is the error term of neuron unit i in thel^(th) layer, and f(p_(i),l) represents the neuron threshold function ofthe neuron potential p_(i),l of the i^(th) neuron in the l^(th) layer.The index L represents the output layer, and α and β are constants. Inparticular, α is the learning gain constant and β is the decay constant.The last term in Eqn. (1) is an optional decay term that is includedprimarily to model intentional or unintentional decay of gratings in aphotorefractive crystal. Other important physical effects includenonlinearities in the response of the medium. For example, withappropriate encoding of data, the photorefractive material can yield anet response of Δw_(ij) ∝sgn(δ_(i) x_(j)) (|δ_(i) x_(j) |)^(1/2), inwhich sgn(u) is equal to +1 if u>0, -1 if u<0, and 0 if u=0. Simulationsindicate that such a nonlinearity can actually improve the performanceof the apparatus during learning. (Most other physical effects such assaturation and non-uniformities in the medium are considered primarilyunintentional and can be treated or accounted for separately.)

Thus, the implementation problem reduces to (1) implementing the weightupdates given in the generic learning technique of Eqn. (1), and (2)generating the terms 6 for the appropriate learning technique. Theformer is the more difficult task, and once it is accomplished, manylearning techniques, the above comprising only a few examples, can beimplemented.

4. Neuron Units and Weight Update Calculation.

Two-dimensional optoelectronic spatial light modulator (SLM) arrays,with integrated detectors, modulators and electronics, as shown in FIG.12, are envisioned for conventional inner product neuron units, as wellas for generation of the δ_(i) terms. This technology provides: (1)incorporation of bipolar signals via two-channel inputs and outputs; (2)slight variants of the same basic SLM structure for all SLMs in thearchitecture (for neuron units and δ_(i) generation); (3) incorporationof different neuron unit functions, including linear, soft threshold,and hardclipping, as well as variable gain; and (4) potentialextendability to future neural network models.

5. Architecture.

The architecture for the case of Hebbian learning, δ_(i) =y_(i), wherey_(i) is the output of neuron unit i, is shown in FIG. 14.(Generalization to other learning techniques is given below.) Onlyfeedforward connections are shown.

The two sets of recording beams 11 and 13 and the components therein arethe same as described in FIG. 6A. Spatial light modulator means 32(x_(j)) provides the inputs to the interconnections; the write input 70of spatial light modulator means 32 (x_(j)) is the input to the neuralnetwork; alternatively, this input can be derived from the previouslayer or module. The output (reconstructed) beams 10' reflect off mirror72, and are imaged via lens 74 onto the write side of spatial lightmodulator 28, after reflecting from beamsplitter 76. Lens 74 in effectimages the output of SLM 28 (virtual image), through the recordingmedium of volume holographic optical element 20, and onto the input ofSLM 28. The combination of detector(s), control electronics, andmodulator(s) that comprise SLM 28 is used to form the array of neuronoutputs y_(i), which are functionally dependent (e.g., by means of athreshold or sigmoid response) on the incoherent weighted sums of theform Σ w_(ij) x_(j) summed over j.

Dove prism 78 serves to flip the beam so that the image orientation atSLM 28 is consistent. Then, the readout beam passing through SLM 28 haspointwise intensity proportional to y_(i), the output of the neuronunits as determined by the weighted interconnections in the layer ormodule depicted in FIG. 14. Output beams 110" are directed to asubsequent module or layer, or can be used to generate outputs of theneural network. Lateral and feedback interconnections are implemented byadding an optical path similar to that of the output beams 10', in thiscase by incorporating a beamsplitter behind holographic element 20, andreflecting a portion of the set of output beams 10' around the bottom ofFIG. 14, to be imaged onto the input side of SLM 32. This provideslateral and feedback connections within holographic element 20. If fixedconnections are desired (as is often the case for lateral connections),while maintaining adaptive feedforward connections, then instead a pathis inserted from behind lens 36 (via a beamsplitter), through a separatehologram, and is imaged onto the input side of SLM 32. The same opticalarrangement is also used when adaptive lateral and/or feedbackconnections that update by a different training technique than thefeedforward connections are desired.

During the computation phase, the shutter 24 is closed to preventlearning. The array of sources is imaged onto SLM 32 as a set of readbeams. Each beam is modulated by SLM 32 to provide the inputs. Then each(reference) beam x_(j) passes through the holographic element 20 toprovide the interconnections, i.e., the weighted fan-out from each inputx_(j). The hologram output is sent to the write side of SLM 28 via thelens 74, at which point the pointwise incoherent sums are detected,functionally transformed, and used as inputs to the modulator(s) withineach individual pixel.

In a number of neural network applications that do not require real timeadaptation, the holographic element may be fixed, obviating the need forrecording capability. In such cases, an important variant of theapparatus shown in FIG. 14 can be configured by: eliminatingbeamsplitter 16, shutter 24, lens 26, spatial light modulator 28, lens30, mirror 22, mirror 72, beamsplitter 76, and Dove prism 78; placingthe source array 14 in the approximate location of mirror 22 andreadjusting the position of lens 34 to image the source array ontospatial light modulator 32; and placing lens 74 in the output beams 10',adjusted to provide coincident 2-D arrays in the desired output plane(not shown). It will be obvious to those skilled in the art that thisreadout system includes means for securing and orienting the volumeholographic element 20 at the position and orientation shown. Such areadout only apparatus is functionally equivalent to the apparatus shownin FIG. 14 when the shutter 24 is closed, as described above, but hasthe advantages of simplicity and reduction in the number of requiredcomponents. Additionally, for iterative (recurrent) neural networks, theoutput beams (10') are sent, reflecting off of a beamsplitter behindholographic element 20, around the bottom of FIG. 14 to be imaged ontothe input side of SLM 32, as described above. Another example of such afeedback arrangement is shown in FIG. 17, described below.

Again with respect to FIG. 14, in the learning phase, the shutter 24 isopen. The weight update term is computed optically (by the spatialmodulation of the set of beams 11 by SLM 28 and by the pairwiseinterference of the object and reference beams) and recorded into thephotorefractive material comprising holographic element 20. Light fromeach source is approximately collimated and used as a read beam for SLM28. Thus, for an N by N array of sources, there are N² beams reading outSLM 28 simultaneously, each at a different angle; all y_(i) terms areencoded onto each of these beams. Each of these beams interferes onlywith its corresponding reference beam, x_(j), from the same source, inthe photorefractive material of holographic element 20. This writes theset of desired weight update terms αx_(j) y_(i).

A generalized architecture for the implementation of neural networks isshown in FIG. 15. The paths and components for recording the hologramsare the same as above, except for the training term generator 80 and anadditional shutter 81 (needed for the implementation of certain neuralnetwork algorithms). The purpose of generator 80 is to opticallygenerate the δ_(i) terms according to the learning technique beingimplemented. In general, there are as many as three different inputsignals to generator 80 (usually at most two of them are needed for agiven learning technique). The input t_(i) on beam 82 is a target ordesired output signal for supervised learning, y_(i) are outputs (andp_(i) are the corresponding potentials) of neuron units at the output ofthe current module. Beams 110" write onto spatial light modulator 84 (inan image plane of the exit plane of generator 80); the SLM is then readout by beams 10" through lens 86 which images SLM 84 onto theappropriate SLM in the generator.

Means for implementing sample learning techniques (for generator 80) areshown in FIG. 16. These implement the well-known (A) Widrow-Hoff, (B)Perceptron, and (C) least mean square (LMS) learning techniques. Allspatial light modulators have differential (positive and negativechannel) inputs and dual channel outputs (both positive and negative).They all have nearly the same circuitry. Spatial light modulator 88provides a linear difference of the inputs; spatial light modulator 90has a higher gain with saturation to provide a binary response; spatiallight modulator 92 provides a non-monotonic function (e.g., Gaussian)for the f'(p_(i)) term. Spatial light modulator 32 in other Figures isthe same as SLM 88, except for a soft thresholding characteristicprovided by the control circuitry and output drivers in SLM 32. For thecase of back propagation (LMS) in a hidden layer, the pair of signalsy_(i) and t_(i) input to each pixel in (C) is replaced by the error termΣ_(k) δ_(k),l w_(ki) from the previous layer. Each layer generates sucherror terms in the following manner. Beams 11 pass through theholographic element 20 and reconstruct additional output beams. Theseadditional output beams contain the information Σ_(k) δ_(k),l-1 w_(ki)and are sent to modulator 88 of the previous layer. It should also benoted that an alternative arrangement can implement multilayer neuralnetworks in a single module of FIG. 15, by directing the output signals110" to the input of SLM 32, using optical feedback to enable multiplepasses through different neuron units and through the same holographicelement 20.

A variant of this architecture can be obtained by exchanging the spatiallight modulators 28 and 32, as shown schematically in FIG. 17. (SLM 28is again replaced by SLM 80 for the general case.) In this case, theupper SLM 32 in FIG. 17 represents the layer inputs x_(j), while thelower SLM 28 represents y_(i). The optical feedback is imaged onto thelower SLM 28. This provides for coherent fan-in at each neuron unitinput. With intensity coding of data, this coherent sum deviates fromneural models, but in some cases may provide an increase in diffractionefficiency to each neuron unit.

In the preferred embodiment, the object SLM 28 performs spatial(parallel) modulation of the object beams, while SLM 32 performsindependent modulation of each reference beam. In the variant describedabove, SLM 32 performs spatial (parallel) modulation of each referencebeam, while SLM 28 performs independent modulation of each object beam.In two additional configurations, both SLMs may perform spatialmodulation, or both SLMs may perform independent modulation. Specificapplications will dictate the particular choice of modulation.

An additional variant of this architecture can be obtained by utilizingthe subhologram version described elsewhere above, in which a lens (notshown) following spatial light modulator 28 is adjusted to focus thetwo-dimensional Fourier transform of each of the beams transmittedthrough spatial light modulator 28 onto spatially separated regions atthe entrance plane of holographic element 20. In addition, lens 36following spatial light modulator 32 is adjusted to image the outputside of spatial light modulator 32 onto the entrance plane ofholographic element 20 in such a manner as to assure registry of theimage so generated with the array of Fourier transforms just described.In this manner, each individual pixel x_(j) is interconnected to thefull set of pixels comprising spatial light modulator 28. As describedpreviously, this configuration can yield high throughput with reducedcoherent recording crosstalk in comparison with the full apertureversion described above.

C. TELECOMMUNICATIONS

Photonic switching networks may be divided into two categories: (1)telecommunications switching and (2) interconnection networks fordigital computing. The primary differences between these two categoriesare in the distance scale and the data bandwidth per channel required bythe application; as a result, telecommunications data channels aretypically carried on optical fibers and have many multiplexed datachannels on each fiber, with wavelength division multiplexing being acommon multiplexing technique. Interconnection networks for digitalcomputing (1) may have data channels on optical fibers or on free-spaceoptical beams, (2) can be much higher bandwidth per channel, and (3)usually do not multiplex more than a few channels on one optical signalline. Local area networks are in between these two realms, and are notdiscussed here, as once the two more extreme cases are illustrated, themiddle ground is a straightforward extension.

In this section, embodiments of the invention are described for theapplication of telecommunication switching networks. It is assumed thatthe input and output optical signals are wavelength divisionmultiplexed, although the embodiments are applicable to a broad range ofchannel multiplexing schemes. The embodiments described are directlyapplicable to circuit switching networks. In this case, it is importantto distinguish between the control signals that are used to set theroutes and state of the switch, and the (high bandwidth) data signalsthat are routed through the switch from an input or source node to anoutput or destination node. In addition, one physical input datatransmission line (i.e., one optical fiber) is referred to herein as adata line, and each individual information channel as a data channel.Thus, many data channels, each at a different optical wavelength, aremultiplexed onto one data line. An array of data lines is input to andoutput from the optical switch.

Photonic switching networks should have the following properties: (1)high bandwidth for the data signals, (2) compatible physicalinterface(s) to the optical input and output lines, (3) compatibilitywith multiplexing schemes utilized for the input and output lines(usually by demultiplexing the input signals and re-multiplexing theoutput signals), (4) capability for implementing a large number of inputand output lines in a relatively compact package, (5) packet and/orcircuit switched control, (6) reconfigurability at a low-to-moderaterate (for circuit switched networks) or at a high rate (for packetswitched networks), and (7) ability to re-route some data signals whileother data channels are being used. In addition, it is desirable to havethe capability for broadcast (fan-out) of a data channel in someapplications, as well as fan-out and fan-in of a physical data line.

The first described embodiment will accommodate a 1-D array ofwavelength division multiplexed (WDM) inputs and a 1-D array of WDMoutputs. The apparatus is shown in FIG. 18. A source array means isprovided at 214; this consists of a two-dimensional array of sources,each at a different center optical frequency ν_(j) along one dimension(e.g., row), with each individual source along the other dimension(e.g., column), all at essentially the same center frequency, butarranged so as to be mutually incoherent, as in previously discussedembodiments. Each center frequency ν_(j) corresponds to the centerfrequency of one optical data channel. Two means for providing thisarray are described below. This source array provides illumination forthe control signals. The set of optical beams from 214 are split bybeamsplitter 16. The reference beams are reflected from beamsplitter 16,pass though shutter 81, through optical means 130 and are additionallyreflected from reflecting means 22. The optics 130 are anamorphic andserve to condense the dimension of different center frequencies ν_(j) toa single pixel at source control means 132, while imaging the dimensionof mutually incoherent sources centered at ν_(j) from 214 to sourcecontrol means 132. At source control 132, means are provided formodulating each pixel independently, and for making the phase frontsleaving 132 substantially identical to the phase fronts leavingwavelength demultiplexer 94. If the modulator in the source controlmeans 132 has a high enough contrast ratio and turns off sufficientlywell, then shutter 81 is not needed. The beams leaving source control132 are made to pass through beamsplitter 96 and optical means 136 thatvery approximately collimates the beams. In the case of focal lengthsand distances being appropriately chosen, optical means 136 can beomitted. The beams are then incident on volume holographic element 20.The source array as modified and passed through source control 132provides the set of reference beam illumination signals for theholographic recording process. The other set of beams from source array214 passes through beamsplitter 16, shutter 24, optical means 126, anddestination control 128 which consists of a spatial light modulator thatserves to input the routing function. The beams are then incident on therecording medium of holographic element 20. Optical means 126 areanamorphic and serve to image the beam in the dimension of the differentoptical center frequencies ν_(j), from the source array 214 to themodulator 128. In the dimension of mutually incoherent sources centeredat ν_(j), optical means 126 serves to direct the beam from each sourcethrough all corresponding pixels of modulator 128 in the corresponding1-D dimension (e.g., column). This completes the control signal portionof the apparatus.

A set of switch states can be loaded into the holographic opticalelement by any of three techniques: (1) sequencing through theone-dimensional array of pixels in source control 132 one at a time,interfering each with appropriate destination control signals frommodulator 128 (thus recording control signals for all wavelengths of agiven input line in one step); (2) sequencing through a set of updatesgiven by the interference of many pixels in source control 132 withpixels in modulator 128, similar to the neural network case describedabove; or (3) a compromise between these two extreme cases. A potentialadvantage of (2) is a decrease in the number of sequences required incertain cases.

The data signals input to the switch and arranged in plane 98 (e.g.,from optical fibers), are sent through an optical wavelengthdemultiplexer 94 (e.g., a grating), reflect off beamsplitter 96 andfollow a substantially identical path from beamsplitter 96 toholographic element 20. The exit plane of demultiplexer 94 is in aconjugate (image) plane of the exit plane of source control 132. Whenthe two sets of control beams from source array 214 are blocked (viashutters or modulator means in source control 132 and modulator 128),only the data signals pass through the holographic element. Afterdiffracting from the recorded interference patterns within holographicelement 20, the output data signal beam passes through optical means 174and 174' to plane 310, which is an image plane of the modulator 128.Then, fiber interface unit 312, which consists of optics and an opticalwavelength multiplexer, multiplexes all wavelengths along the opticalcenter frequency ν_(j) dimension, in order to yield the one-dimensionalwavelength division multiplexed output at data output plane 314. Anoptical fiber array, for example, can be arranged following output plane314 to receive the re-routed and re-multiplexed data signals from thedata inputs arranged at plane 98; these routing and multiplexingfunctions can include channel broadcast, line broadcast, and line fan-infunctions.

Once established, the routes through the switch can be changed all atonce by erasing the holographic recording material and then recordingthe new interconnection pattern. Individual routes can selectively bechanged by either of two techniques: (1) not refreshing the old routesto be changed, which will then decay in time, and refreshing the newroutes; or (2) erasing specific gratings using binary phase modulationin 128 and 132; such phase modulation to selectively erase gratings hasbeen previously demonstrated; see, e.g., A. Marrakchi, Optics Letters,Vol. 14, No. 6, pp. 326-328 (Mar. 15, 1989).

Two alternative means for providing the source array 214 are describedherein. In FIG. 19A, a two-dimensional array of sources 316 is shown, inwhich the center optical frequency is varied along dimension 318, andthe mutual incoherence of the sources with essentially the same centerfrequency is provided along dimension 320. This can be accomplished, forexample, by providing an array that is designed to implement thewavelength variation in one dimension of the array, with typicalprocessing-induced stochastic variation providing the required mutualincoherence in the second dimension. This array can then be useddirectly in source array distribution plane 214.

Another means for providing the source array distribution 214 is shownin FIG. 19B. In this case, two one-dimensional arrays are used. Element322 is a one dimensional array of sources, e.g. laser diodes, each witha different optical center frequency ν_(j), and can be fabricated as aone-dimensional version of source array 316. Optics 324 expands thebeams in the dimension perpendicular to 322, and condenses in thedimension of source array 322 before passing through one-dimensionalphase modulator 326. Each pixel of modulator 326 provides phasemodulation at a different frequency, and can be fabricated as aone-dimensional version of the pixelated piezoelectric mirror or purephase modulator array described previously in Section A2. Optical means328 then expands the result in the orthogonal dimension, therebyproducing a two-dimensional array, which can then be used as the inputsource array 214. The optical means 324 and 328 in FIG. 19B areessentially the same as those of an analog optical outer product matrixprocessor (R. A. Athale, Proceedings of the Tenth International OpticalComputing Conference, IEEE Catalog No. 83CH1880-4 pp. 24-31, April1983). It will be noted that in this case, the beamsplitter 16 can beinserted before the plane S_(i) (but after phase modulator 326); thiswill make the overall system more compact.

Referring now to the case of two-dimensional WDM data input lines andtwo-dimensional WDM data output lines, the apparatus is again shown inFIG. 18, but the following components have different functions thanthose described for the case of one-dimensional data signals. The sourcearray 214 is a two-dimensional array, each element of which has adifferent frequency modulation imposed on it in order to produce mutualincoherence among all the source elements; each element of the sourcearray 214 contains beams of all center frequencies ν_(j), whichcorrespond to the center frequencies of each data signal channel. Meansfor providing this are described below. In the case of applications thatdo not require data channels to fan in and do not require output datachannels to be angularly multiplexed, the mutual incoherence is notrequired; only means for amplitude modulating individual elements arerequired. Optical means 130 now image from source array 214 to themodulator plane in source control 132. The source control 132 consistsof both an optical wavelength demultiplexer and a two-dimensionalmodulator. Optical means 136 again very approximately collimates thebeams. Optical means 126 directs the light from each pixel of sourcearray 214 through every pixel of the modulator in destination control128. The destination control 128 now includes an optical demultiplexer(e.g., grating). The data inputs at plane 98 are now arranged in atwo-dimensional array, as are the data outputs at plane 314. Opticalmeans 312 is now simpler than that required for the previously discussedembodiment, as all of the reconstructed pixels are imaged by holographicelement 20 and optical means 174, 174' onto the correct locations foroutput at plane 310.

In a number of telecommunication switching applications that do notrequire real time reconfiguration capability, the holographic elementmay be fixed, obviating the need for recording capability. In suchcases, an important variant of the apparatus shown in FIG. 18 can beconfigured to eliminate beamsplitter 16, shutters 24 and 81, opticalmeans 126, destination control 128, and mirror 22 by placing the sourcearray 14 in the approximate location of mirror 22, and placing opticalmeans 130 between the source array and spatial light modulator 132 insuch a way as to image the source array onto spatial light modulator132. It will be obvious to those skilled in the art that this readoutsystem includes means for securing and orienting the volume holographicelement 20 at the position and orientation shown. Such a readout onlyapparatus is functionally equivalent to the apparatus shown in FIG. 18when shutter 24 is closed and shutter 81 is open, as described above,but has the ad vantages of simplicity and reduction in the number ofrequired components.

Means for providing the source array signals are shown in FIG. 20. Atwo-dimensional source array (e.g., surface emitting laser diodes) 330provides an array of sources, each at a different center frequencyν_(j). Optical means 332 directs the light from each source element toall pixels of the two-dimensional modulator array 334. Each pixel ofmodulator array 334 provides phase modulation at a different frequency,and can be fabricated as the pixelated piezoelectric mirror or purephase modulator array described in Section A2. Modulator array 334 thenprovides the optical signals of plane 214 as depicted in FIG. 18. Asdiscussed above, in the common case of applications that do not requiredata channels to fan in and do not require output data channels to beangularly multiplexed, the mutual incoherence is not required. In thiscase, modulator array 334 provides the requisite amplitude modulation.Furthermore, in most such applications, binary amplitude modulation issufficient. If optical means 332 is provided by simple (non-multiplexed)elements, such as a simple beam expander (e.g., lens), then an opticalwavelength multiplexer 336 (e.g., set of gratings) is incorporated asshown. Its function is to fan in the beams of different centerfrequencies to be collinear at each pixel.

Finally, it should be noted that by more precisely collimating the beamsat the holographic element 20 and by choosing center frequencies ν_(j)appropriately, the apparatus described above can be extended to atwo-color system in which the data signals read out the storedholographic interconnections non-destructively. In this case, thegeometry and scaling of the optical data paths are changed relative tothose of the optical control signal paths.

D. DIGITAL COMPUTING

For the application of digital computing interconnections, it is assumedthat the inputs and outputs are not wavelength division multiplexed,such WDM cases having previously been discussed above. Further, they canbe input to, and output from, the interconnection network in the form ofoptical fibers or as free space beams that are imaged from one plane toanother.

In the case of optical fibers, a photonic system for a crossbarinterconnection network can be explained using FIG. 18, in which thefollowing components are interpreted differently than in thetelecommunications application previously described. The data inputs andoutputs are arranged in 2-D arrays. The source array 214 is a 2-D arrayof individually coherent but mutually incoherent sources, as describedabove. Here they all have the same center wavelength. The remainingcomponents in FIG. 18 are the same as in the telecommunicationsswitching apparatus, for the case of 2-D data input and output arrays,with the exceptions detailed herein. Since the input and output data arenot wavelength multiplexed, the wavelength multiplexers anddemultiplexers in wavelength demultiplexer 94, destination control 128,and output fiber interface unit 312 are not needed. The output fiberinterface unit 312 comprises only the optical element(s) needed tocouple the light into each fiber.

The control procedure for recording the interconnections is the same asin the telecommunications embodiment above, except that there is nowavelength dimension. Control can again be accomplished by making arecording for each single pixel of SLM 132, interfering with light fromall destination control pixels of SLM 128. Alternatively, all pixels ofboth SLMs can be used during each recording cycle, in effect summingover a set of matrices of rank one to build up an interconnectionpattern, similar to the neural case.

In a number of digital computing applications that do not require realtime reconfiguration capability, the holographic element may be fixed,obviating the need for recording capability. In such cases, an importantvariant of the apparatus shown in FIG. 18 can be configured to eliminatea number of components, as described above for the case oftelecommunications switching. Such a readout only apparatus isfunctionally equivalent to the apparatus shown in FIG. 18 when shutter24 is closed and shutter 81 is open, but has the advantages ofsimplicity and reduction in the number of required components.

An extension of this apparatus utilizing the copying technique describedherein enables faster computing. Two volume holographic recording mediaare employed. The primary holographic medium is used for the actualcomputation, and a secondary holographic medium is used to record theset of interconnection patterns from the control inputs. When therecording of a set of new interconnection patterns into the secondarymedium is completed, it is copied into the primary medium in a singlestep. In this way, computation is being performed while the next set ofinterconnections is being configured. While recording of a newinterconnection configuration can take some time, the copying can takeplace in one step. This minimizes the net reconfiguration time of theswitch.

The same apparatus can be used for free space data inputs and outputs,by removing interface unit 312. Note that this is in effect ageneralized crossbar, in that it not only allows arbitrary 1-to-1interconnection, but also enables fan-out and fan-in. In addition, atwo-wavelength system can be employed, as in the two-colortelecommunication application, by changing the scaling and geometry ofthe optical data paths relative to the optical control signal paths.This enables non-destructive readout.

E. HOLOGRAPHIC OPTICAL ELEMENTS

As described throughout the present application, volume holographicoptical elements can be employed in a large number of interconnectionand memory applications. Of particular concern to the presentapplication are those volume holographic optical elements that areeither recorded by (or can be recorded by) the incoherent/coherentdouble angularly multiplexed techniques described in this applicationand its parent and grandparent applications, or incorporate computergenerated holograms that emulate the functionality of such elements inthat they can be used directly in at least one of the architecturesdescribed herein.

This specific class of novel volume holographic optical elements ischaracterized by a number of distinctive features, as might beanticipated from the novel incoherent/coherent double angularlymultiplexed recording technique itself. In particular, the holographicmodulation pattern that is recorded (or in certain cases, computergenerated) within the volume holographic optical element comprises amultiplexed set of individual modulation pattern components.

For the specific case of an optically recorded holographic modulationpattern, each individual modulation pattern tern component comprises theholographic interference pattern generated by a single source elementwithin the individually coherent, mutually incoherent source array(e.g., source array 14 in FIGS. 4, 5, 6A, 6B, 7, 14, 15, 17, 21, and 22;source array 214 in FIG. 18, source array 316 in FIG. 19A, source array322 in FIG. 19B, and source array 330 in FIG. 20).

We further distinguish between two recording scenarios within this caseof an optically recorded holographic modulation pattern. For thescenario of simultaneous (single-exposure) recording of a multiplexedholographic element using a set of sources, the resulting multiplexedholographic modulation pattern comprises a holographic record of the setof mutually incoherent optical interference patterns, one suchinterference pattern deriving from each source. For the scenario ofsequential (multiple-exposure) recording of a multiplexed holographicelement using only one source at a time, each component of the resultingmultiplexed holographic modulation pattern comprises a holographicrecord of the interference pattern resulting from each source. In anideal holographic material, the resulting multiplexed holographicelements in the two cases would be identical. In physically realizableholographic materials, the resulting holographic elements will differdue to effects such as history-dependent material sensitivity, partialerasure, and nonlinearities in the material response and in therecording and reconstruction processes.

For the specific case of computer generated holograms, each individualmodulation pattern component (whose modulation pattern is calculated bycomputer) is configured to function within at least one of thearchitectures described in this application or in the parent applicationin such a manner as to emulate the performance characteristics of theoptically recorded modulation patterns described above. In some cases,it may prove advantageous to further optimize the aggregate computergenerated hologram comprising the multiplexed set of individualmodulation pattern components against one or more specific performancemetrics (such as throughput or crosstalk minimization).

These individual modulation pattern components, insofar as they arederived from and function within the incoherent/coherent doubleangularly multiplexed nature of the architectures described in thepresent and parent applications, exhibit specific characteristics thatare unique to the best of the inventors' knowledge when taken in theaggregate. When illuminated by the associated reference beams (derivedfrom the set of individual sources described above within the sourcearray for the case of the recording and readout configurations, and fromthe corresponding set of sources within the source array for the case ofthe readout only configurations), diffraction from the multiplexed set(or any subset thereof) of individual modulation pattern componentsgenerates a set of reconstructed beams such that:

(i) the reconstructed beams emanate from the holographic medium in sucha manner as to be at least partially angularly multiplexed;

(ii) each individual reconstructed beam is encoded with a spatial arrayof pixels that comprise a real or virtual image at some plane in space;and

(iii) the set of images encoded on the set of reconstructed beams can bemade to be substantially coincident in a common plane in space withappropriate optical means.

It should be noted that information can be physically represented ineach such spatial array of pixels as field amplitude, phase, or acombination of both. In the case of both amplitude and phaserepresentation, each individual modulation pattern component can be aholographic record of the interference pattern of a 3-D object.

As described above, in reference to FIGS. 4, 5, 6A, and 6B, and inreference to the master holographic element in the copying apparatus,the simultaneous spatial modulation of angularly multiplexed mutuallyincoherent beams (as depicted in FIGS. 6A, 6B, 14, 15, 17, 18, and 21)enables an imaging system to superimpose the beams emanating from theresulting holographic element at some plane in space. This in turnenables a pixel-by-pixel incoherent summation to be performed in such aplane by means of an appropriate two-dimensional detector array. Moreconventional volume holographic element multiplexing techniques do notprovide for angular multiplexing of the object beams simultaneously withthis coincident-array imaging capability.

A wide variety of additional types of holographic optical elements(HOEs) are used in optical systems and may include such elements asmulti-focal length lenses, specific combinations of wavelengthdispersive and wavefront-modifying optical elements, and for purposeshere, also holographic elements for display. Examples include, but arenot limited to, head-up displays (HUDS), dichroic beamsplitters,aberration-corrected lenses, multi-function beamsplitters, multiplefocal length lenses, and space-variant optical elements.

Advantages of HOEs over conventional optical elements include reducedsize, weight, and cost; additionally, in some cases, there are nopractical alternatives to certain HOEs. Furthermore, if the HOE can berapidly copied, then a large savings in production cost can be achieved.

A volume holographic optical element can store a large amount ofinformation; the process of recording all of the needed information intothe volume can be a significant bottleneck in both initial developmentand production. In the present application, three realms are discussed:(1) that of recording complex fringe patterns in the holographicrecording medium that correspond to combinations of optical elements, sothat the phase fronts can be generated relatively easily and recordedrelatively quickly; (2) a computer aided approach in which a series ofexposures is cycled through in order to build up the requisiteinterference fringe pattern in the holographic recording medium; and (3)a computer generated hologram approach in which the functionalperformance characteristics of the holographic optical element are usedto calculate corresponding individual modulation pattern components thatcan be incorporated into planar, contiguous multilayer or stratifiedmultilayer volume holographic media by photolithographic, electron beamlithographic, or other similar techniques.

In the second case, the input patterns used for each exposure aregenerally calculated by computer or neural network. However, if theinput patterns are known a priori, and a suitable input device isavailable, no computations of the fringe pattern need be made. Anexample of this is a multiplexed holographic display in which eachhologram to be displayed consists of a page of information.

An example of the first case is depicted in FIG. 21. Two types of HOEsare discussed herein that can be generated from this apparatus. First,consider a HOE that functions as a space-variant lens, focusing incidentplane waves at different distances z, the distance depending on theincident angle of the plane wave. The array of sources 14 generates aset of coherent but mutually incoherent beams, which are split into twopaths. The upper path carries the reference beams in this case; they aretransmitted by beamsplitter 16 and pass through optical means 226 toholographic element 20. The spatial light modulator 228 is not neededfor the exposure of this particular HOE. Optical means 226 essentiallycollimates each beam. For response to other than collimated beams,optical means 226 can be changed to provide the appropriate focal power.The lower path functions to carry the set of object beams.

After reflecting from beamsplitter 16, optical means 230 approximatelyimages the source array 14 onto each pixel of modulator 232. In thiscase, modulator 232 is a static or dynamic planar microlens array. Thisarray provides a different and programmable focal power for each sourcebeam. Optical means 236 is used to convert the spherically expandingwaves to spherically contracting waves, and to provide relay optics whenneeded.

Upon reconstruction, plane waves incident on the holographic element atthe angles of the upper beam paths utilized during recording areconverted to spherically contracting waves of different focal lengths,thus providing a highly multiplexed lens with space-variant focallength.

In order to generate a space-variant lens capable of convertingspherically expanding waves to spherically contracting waves, theapparatus of FIG. 22 can be used. It is the same as the apparatus ofFIG. 21, except that in this case, the upper path passes through opticalmeans 350, which approximately images the source array onto themodulator 228. Means are provided by modulator 228 to modulate eachimaged element of the source array in focal power (e.g., by means of adynamic microlens array) to produce the desired space variant focallength HOE. Certain other applications require modulator 228 to modulatephase, or amplitude and phase, instead of focal power.

Another mode of recording permits a larger fraction of the aperture ofholographic element 20 to be utilized for each point-spread functionresponse of a space-variant HOE; it uses the apparatus of FIG. 21. Thismode can be utilized to record essentially arbitrary phase fronts thathave values at each pixel between 0 and 2π. An example of such anoptical element is a multiplexed HOE that stores Fresnel lenses ofseveral different focal lengths; note that this can include sphericalFresnel lenses as well as anamorphic Fresnel-type lenses, and other evenless symmetric phase fronts. In this mode, the upper path carries theobject beams and the lower path carries the reference beams.

The modulator 228 is a spatial light modulator that modulates phase ateach pixel; modulator 232 is an amplitude spatial light modulator and isused to set the diffraction efficiencies of each recorded hologram.Optical means 236 is configured to produce a set of multiplexedreference beams that are substantially identical to the anticipatedcollection of reference beams to be utilized during reconstruction.During exposure, in one embodiment the individual sources in sourcearray 14 are turned on one at a time, and the desired object pattern iswritten onto modulator 228 for each source. If the same pattern atmodulator 228 is to be used for multiple sources (i.e., to recordmultiple holograms), then those sources pertaining to a common objectpattern can be turned on simultaneously, reducing the requisite numberof recording steps. Depending on the application, this can result inconsiderable or even dramatic savings in recording time. In the fullysequential case, the described apparatus utilizing the two-dimensionalsource array still has the advantage of permitting recording of theentire multiplexed HOE without any moving parts.

For reconstruction, the HOE is illuminated with reference beamssubstantially identical to those used during exposure, except that theymay be independently and arbitrarily amplitude modulated. The outputbeams then give the desired phase front patterns according to the objectpatterns that were recorded. This provides a space-variant HOE in whichthe point-spread function response can be chosen essentiallyindependently for each pixel of an input array. For applicationsrequiring space-invariance over small local regions of the input plane,the same object pattern can be recorded for reference beamscorresponding to neighboring pixels in the input array, oralternatively, the hologram thickness is chosen appropriately and fewerrecording beams are used, yielding space-invariance within the Braggangle of a particular hologram.

According to the teachings of the invention, it will be appreciated thatseveral additional methods of multiplexing can be utilized to advantageduring the recording of holographic optical elements, including angular,spatial, and/or wavelength multiplexing of both the object and referencebeams.

It will also be noted that for certain appropriate applications, theupper path of the apparatus may be interpreted as carrying the referencebeams, and the lower path may be interpreted as carrying the objectbeams. Then, during reconstruction, when beams of appropriate phasefronts are incident on the holographic medium, the output beamsreconstruct spots in an image plane of optical means 232. Eachreconstructed spot then has a value proportional to the similarity ofthe incident wavefront to one of a set of stored basis functionwavefronts. (These basis function wavefronts are dependent both on theinput patterns and on the angle of each such reference beam duringrecording.) Appropriate applications include, but are not limited to,associative memory, optical correlation, optical pattern recognition,and optical feature extraction.

Finally, consider the case of a sequence of exposures, in which thedesired object patterns are not input directly, but rather are designedsuch that the resultant recorded holographic fringe pattern, at thetermination of the exposure sequence, produces upon reconstruction thedesired output functions. In this case, it is in general desirable tomodulate both the phase and amplitude of the incident beams, which canbe implemented with a spatial light modulator characterized byindependent control over both amplitude and phase in each individualpixel, as described above; however, it should be noted that a largeclass of patterns can be recorded with either phase modulation only, orwith amplitude modulation only. In this operational mode, the designedset of object patterns can be produced either by computer aided designtechniques (for cases in which the desired holographic recording patternis either known or can be computed with reasonable resources), or by aneural-like learning rule in which a sequence of weight updates areproduced in response to a set of training patterns. In the latter case,supervised learning algorithms are exploited when desired outputpatterns can be represented, and unsupervised learning algorithms areexploited otherwise. The neural technique permits the HOE to converge toan approximate version of the desired HOE, without knowledge of thestored fringe pattern within the holographic medium.

F. OPTICAL INFORMATION PROCESSING

A wide variety of applications to optical information processing can beenvisioned that are based on the novel features of theincoherent/coherent double angularly multiplexed architectures describedin the present, parent and grandparent applications, as well as on thenovel features of the volume holographic optical elements derivedtherefrom. These applications include, but are not limited to,multidimensional correlations (see, for example, E. G. Paek et al,"Compact and Robust Incoherent Holographic Correlator Using aSurface-Emitting Laser-Diode Array", Optics Letters, Vol. 16, No. 12,pp. 937-939, 1991) and convolutions (including both time-integrating andspace-integrating configurations), pattern recognition, featureextraction, image processing, synthetic aperture radar image formation,implementation of nonlinear transformations, cryptography, opticallycontrolled phased array radar, holographic nondestructive testing, andmedical diagnostic applications such as computer-aided tomography andimage segmentation.

Common to many of these applications is the need for implementation ofan arbitrary space-variant point spread function across atwo-dimensional input or output image field. A key advantage of theincorporation of the teachings of this invention in such optical imageprocessing applications is the capability for incorporating just such anarbitrary space-variant point spread function in a volume holographicoptical element with overall high optical efficiency and lowinterchannel crosstalk among the various arbitrary space-variant pointspread function components. The basic principle involved is astraightforward extension of the incoherent/coherent double angularlymultiplexed architecture shown schematically in FIGS. 6A and 6B, inwhich each pixel in spatial light modulator 32 can be interconnectedwith an arbitrary distribution of pixels in spatial light modulator 28by, for example, sequential recording. At each step of the sequence, thedistribution of pixel transmittances in spatial light modulator 28establish the point spread function with the corresponding individualpixel in spatial light modulator 32. Other methods of generating thedesired point spread functions can include neural network trainingsequences, in which the optimal point spread functions are not known apriori and are instead derived from the aggregate of the trainingexperience.

In addition to the capability for implementation of arbitraryspace-variant point spread functions in conjunction with high throughputefficiency and low interchannel crosstalk, several other key advantagesaccrue to the utilization of the teachings of the invention in opticalinformation processing applications. These advantages include thesuperposition of multiple images in the output plane, which in turnallows for efficient use to be made of the space-bandwidth product of atwo-dimensional detector array (with a fixed number of pixels); theutilization of incoherent summation of output images, which eliminatesthe deleterious effects of coherent noise and allows for summation rulesthat are linear in intensity; the capability for single step copying ofcomplex application-specific volume holographic optical elements, whichin turn allows for efficient manufacturing of such devices; and thelarge number of degrees of freedom inherent in the high storage capacityof volume holographic optical elements recorded in accordance with theteachings of the invention.

G. OPTICAL MEMORY

Further in accordance with the teachings of the invention, theincoherent/coherent double angular multiplexing technique specified inthe present, parent and grandparent applications and embodied in thevarious architectures described therein can be utilized to advantage ina number of distinct optical memory applications. Such applicationsinclude, but are not limited to, associative memories (see, for example,E. G. Paek and A. Von Lehman, "Holographic Associative Memory forWord-Break Recognition", Optics Letters, Vol. 14, pp. 205-207, 1989),content-addressable memories, location-addressable memories,page-addressed memories, shared memories and memory systems, andmulti-port memories.

Common to many such optical memory applications are the need forinformation storage (provided by the volume holographic opticalelement); for location-addressable, page addressable, orcontent-addressable information access; for a high signal-to-noise ratio(or equivalently a low bit error rate); and for read/write capability.All of these characteristics are provided by the incoherent/coherentdouble angularly multiplexed architecture and its variants as describedin the present application and its parent.

The implementation of an optical memory system (see, for example, E. G.Paek et al, "Compact and Ultrafast Holographic Memory Using aSurface-Emitting Microlaser Diode Array", Optics Letters, Vol. 15, No.6, pp. 341-343, 1990, and E. G. Paek, "Holographic Memory Read By aLaser Array", U.S. Pat. No. 4,988,153, Jan. 29, 1991) that is based onthe unique features provided by the incoherent/coherent double angularlymultiplexed architecture and its variants is straightforward, based onthe teachings of this invention, as can be easily appreciated by oneskilled in the art. The information storage function can be implementedin accordance with the teachings of the invention by utilizing thearchitecture described in FIGS. 6A and 6B. Enabling of a single pixel inspatial light modulator 32 in conjunction with a set of pixels inspatial light modulator 28 gives rise to a straightforwardimplementation of a page- (or sub-page-) addressable memory. Enabling ofmultiple pixels with either binary or analog transmittances in spatiallight modulator 32 in conjunction with a set of pixels in spatial lightmodulator 28 gives rise to a straightforward implementation of anassociative memory. Both shared and multi-port memories can beimplemented by utilizing more than one spatial light modulator 32 inconjunction with one or more spatial light modulators 28 that access acommon volume holographic optical element. Shared and multi-port memorysystems can be configured by further incorporating more than one volumeholographic optical element in the system.

Common to the optical memory configurations described above are at leasttwo possible configurations for information access (readout). In thefirst such configuration, spatial light modulator 32 receives as itsinputs the output of an appropriate interconnection (routing orcontrolling) network, that in turn determines the key to both information storage and retrieval. In the second such configuration,spatial light modulator 32 is either not incorporated or is set to theuniform transmittance state, and source array 14 is configured in such amanner as to be individually addressable, such that it receives as itsinputs the output of an appropriate interconnection (routing orcontrolling) network, that in turn determines the key to bothinformation storage and retrieval. Additionally, spatial light modulator28 can be used at the output of an interconnection network, while anindividually-controllable source array 14 (or spatial light modulator32) is operated by a separate set of control inputs to access differentblocks within the memory.

In an important variant of the basic single holographic elementconfiguration, the optical memory can be configured as a resonatorstructure in which information is copied from a first volume holographicoptical element to a second, and then from the second volume holographicoptical element to the first, as described in section A3 on copyingapparatus and techniques.

A number of distinct advantages accrue to the use of the volumeholographic optical elements and associated incoherent/coherent doubleangularly multiplexed architectures described in the present, parent andgrandparent applications, as applied specifically to optical memoryapplications. These advantages include high density information storagewith high throughput efficiency and low interchannel crosstalk; thesuperposition of multiple images in the output plane, which in turnallows for efficient use to be made of the space-bandwidth product of atwo-dimensional detector array (with a fixed number of pixels); theutilization of incoherent summation of output images that are inregistry in a common plane, which allows for the incorporation ofthreshold or other logic at each detector location in the output plane,eliminates the deleterious effects of coherent noise, and allows forsummation rules that are linear in intensity; information access at highdata transfer rates due to the inherent incorporation of parallelaccess; low latency information retrieval, as determined either by thespatial light modulator rise time, or the rise time of one or moreelements of the individually addressable source array; the provision foranalog as well as digital information storage; the capability for singlestep copying of complex application-specific volume holographic opticalmemory elements, which in turn allows for efficient manufacturing ofsuch devices; and the large number of degrees of freedom inherent in thehigh storage capacity of volume holographic optical elements recorded inaccordance with the teachings of the invention.

INDUSTRIAL APPLICABILITY

The present invention is expected to find use in neural networks,telecommunications, digital computers, optical signal processors,optical information processors and computers, optical memories, andholographic optical elements.

What is claimed is:
 1. A multiplexed volume holographic optical elementreadout apparatus, comprising:(a) means for providing a two-dimensionalarray of individually coherent light sources that are mutuallyincoherent; (b) means for forming a reference beam from eachindividually coherent light source, thereby forming a multiplexed set ofreference beams; (c) means for modulating each said reference beam,thereby forming a multiplexed set of modulated reference beams; and (d)means for directing at least a portion of said multiplexed set ofmodulated reference beams to a predetermined location.
 2. The apparatusof claim 1 further including optical detection means.
 3. The apparatusof claim 1 wherein said array of individually coherent light sourcescomprises an array of semiconductor laser diodes, each saidsemiconductor laser diode itself coherent and operating incoherentlywith respect to at least one of the other said semiconductor laserdiodes within said array.
 4. The apparatus of claim 1 wherein saidmultiplexed set of reference beams is multiplexed in at least one ofangle, space, and wavelength.
 5. The apparatus of claim 4 wherein eachsaid reference beam is at a separate given angle.
 6. The apparatus ofclaim 1 wherein each said reference beam is independently modulated. 7.The apparatus of claim 1 wherein each said reference beam is spatiallymodulated so that all said reference beams are identically modulated. 8.The apparatus of claim 1 wherein said means for modulating each saidreference beam comprises a spatial light modulator.
 9. The apparatus ofclaim 8 wherein said spatial light modulator comprises an array ofintegrated optical detectors, optical modulators, and associatedelectronics, said detectors capable of detecting at least one controlbeam incident thereon to generate a detected signal, said modulatorscapable of modulating said set of reference beams, and said electronicscapable of processing said detected signal and controlling the amount ofmodulation of said modulators.
 10. The apparatus of claim 1 wherein saidmeans for modulating each said reference beam comprises a planarholographic optical element.
 11. The apparatus of claim 1 wherein saidmeans for modulating each said reference beam comprises a volumeholographic optical element.
 12. The apparatus of claim 1 wherein saidmeans for modulating each said reference beam comprises independentcontrol of each individual source of said array of individually coherentbut mutually incoherent sources.
 13. The apparatus of claim 1 furtherincluding means for selecting at least a portion of said multiplexed setof modulated reference beams.
 14. The apparatus of claim 13 wherein saidselecting means is provided by independent control of said individuallycoherent but mutually incoherent light sources.
 15. A multiplexed volumeholographic optical element readout apparatus, comprising:(a) means forproviding an array of coherent light sources that are mutuallyincoherent, said means comprising:(i) provision for inputting at leastone coherent beam, (ii) a first acousto-optic deflector, storing a setof moving gratings, each grating having a different spatial frequency,and (iii) means for directing at least one said coherent beam onto saidfirst acousto-optic deflector, thereby generating a set of output beams;(b) means for forming a reference beam from each said coherent lightsource, thereby forming a multiplexed set of reference beams; (c) meansfor modulating each said reference beam, thereby forming a multiplexedset of modulated reference beams; and (d) means for directing at least aportion of said multiplexed set of modulated reference beams to apredetermined location.
 16. The apparatus of claim 15 further comprisingmeans for optically transforming said set of output beams, such that anarray of self-coherent but mutually incoherent source beams isgenerated, each at a different angle.
 17. The apparatus of claim 15further comprising:(a) a second acousto-optic deflector, orientedorthogonally to said first acousto optic deflector; and (b) means fordirecting said output beams onto said second acousto-optic deflector,thereby generating a set of beams emanating from said secondacousto-optic deflector that are angularly multiplexed in twodimensions.
 18. The apparatus of claim 1 further comprising means forsecuring and orienting a volume holographic optical element in saidpredetermined location.
 19. The apparatus of claim 15 further comprisingmeans for securing and orienting a volume holographic optical element insaid predetermined location.